CN100473062C - Filtering device and method for saving memory space in eight-phase shift keying device - Google Patents

Abstract

The invention relates to a filtering device for an eight-phase-shift keying system. The filtering device comprises a pi/16 phase rotation module, a weight distribution module and a combination module. The pi/16 phase rotation module is used for rotating a second vector generated by a 3 pi/8 phase rotation module at present by an angle of pi/16 again to generate a corresponding third vector. The weight distribution module performs weight distribution on a preset distribution waveform by using a plurality of selected weights and stores the weight distribution waveform as a plurality of corresponding weight distribution waveforms. The combination module determines which weight distribution waveforms to select from the weight distribution module according to the currently generated third vector, and combines the selected weight distribution waveforms to generate a set of modulation signals. The filtering device and the method can greatly save the memory space required in the filtering program.

Description

Filter device and method for saving memory space in eight-phase phase-shift keying device

technical field

The present invention relates to a filtering device and method, in particular to a filtering device and method applied to mobile communication devices.

Background technique

In order to improve the data processing capabilities of existing mobile phones and base stations, wireless system developers are developing so-called 2.5G technology, which enables wireless communication operators to provide voice and high-speed data services to users without replacing the entire telecommunication infrastructure.

An important technology that has aroused the interest of 2.5G system developers is the enhanced data rate GSM (Enhanced Data for GSM Evolution, EDGE) specification, which uses an improved eight-phase phase-shift keying (8PSK) modulation method. EDGE is an innovative technology for the current GSM system, which can provide data transmission rates up to 384kbps, enabling the system to simultaneously provide voice, data, Internet connection and other interconnection solutions. And GSM5.04 provides the specification for eight-phase phase-shift keying modulation mode.

Please refer to the provisions of the GSM5.04 (V8.0.8) protocol for the eight-phase phase-shift keying (8PSK) modulation method in EDGE. According to this agreement, the signal modulation method of the so-called eight-phase phase-shift keying can generally be divided into three types: One step: first, the input is to be mapped by a Gray code (Gray mapping), then a 3π/8 phase rotation is performed, and finally an output is obtained through a filtering process, which is provided to a subsequent radio frequency system to generate a corresponding RF signal.

Please refer to FIG. 1 and FIG. 2. FIG. 1 is a schematic diagram of conversion of well-known digital bits into a first vector through Ray code mapping, and FIG. 2 is a schematic diagram of conversion of the first vector in FIG. 1 into a second vector through 3π/8 phase rotation. The input of the eight-phase PSK system is a series of digital bits, and each group of three digital bits (d _3i , d _3i+1 , d _3i+2 ) will be processed as a signal processing unit. The eight-phase phase-shift keying system converts a group of three digital bits into a first vector (S _i =e ^j2πl8 ) after Gray code mapping, and this first vector is converted into a first vector through 3π/8 phase rotation two vector $({\hat{S}}_i=S_i\&CenterDot;e^{\mathrm{the\; <figure-callout\; id="3"\; label="ji"\; filenames="C03142349E00221.png,C03142349E00231.png"\; state="\{\{state\}\}">ji</figure-callout>}3\mathrm{\&pi;}/8}),$ The second vector is output as a set of modulated signals (Ii, Qi) through a filtering process. This group of modulated signals is the output of the eight-phase phase-shift keying system, which can be regarded as a base frequency signal. The baseband signal can be provided to a radio frequency system for signal modulation in order to generate a radio frequency signal suitable for wireless communication transmission. This group of modulation signals (Ii, Qi) can also be called y(t′), which can be simply expressed as:

其中，T为一个符号周期。

Wherein, T is a symbol period.

In the above representation, y(t′) can be understood as the result of multiplying multiple second vectors by corresponding pre-selected allocation waveforms or filter coefficients Co(t), and then summing them up.

Contents of the invention

The invention is a filtering device and method for an eight-phase phase-shift keying (8PSK) device.

The eight-phase phase-shift keying (8PSK) device includes a Gray code mapping module, a 3π/8 phase rotation module and a filtering device. The Gray code mapping module is used to map each triplet of digital bits into a corresponding first vector through a predetermined mapping program. The 3π/8 phase rotation module is used to rotate the phase of the first vector currently generated by the Gray code mapping module through a predetermined phase rotation procedure to generate a corresponding second vector. The filtering device is used to perform a filtering procedure, and filter the second vector currently generated by the 3π/8 phase rotation module to generate a set of corresponding modulation signals in the plurality of sets.

The filter device of the present invention includes a π/16 phase rotation module, a weight distribution module and a combiner module. The π/16 phase rotation module is used to rotate the second vector generated by the 3π/8 phase rotation module by an angle of π/16 again to generate a corresponding third vector. The weight distribution module performs weight distribution on a predetermined distribution waveform with a plurality of selected weights and stores them as a plurality of corresponding weight distribution waveforms. The combination module generates the set of modulation signals (Ii, Qi) according to the currently generated third vector.

The invention relates to an improvement on an eight-phase phase-shift keying (8PSK) device and method. Due to the improvement of the filtering program, compared with the prior art, the present invention can greatly save the memory space required in the filtering program.

The advantages and spirit of the present invention can be further understood through the following detailed description of the invention and the accompanying drawings.

Description of drawings

FIG. 1 is a schematic diagram of conversion of well-known digital bits into a first vector through Gray code mapping.

FIG. 2 is a schematic diagram of converting the first vector in FIG. 1 into a second vector through 3π/8 phase rotation.

FIG. 3 is a schematic diagram of the filtering device 20 of the present invention and the eight-phase PSK system applying the present invention.

FIG. 4 is a schematic diagram of an angle of π/16 rotation of the π/16 phase rotation module shown in FIG. 3 .

Fig. 5 is a schematic diagram of a combined module in the filtering device of the present invention.

FIG. 6 is a schematic diagram of the predetermined allocation waveform in the filtering device of FIG. 5 .

FIG. 7 is a distribution waveform of filter coefficient Co(t) to 5T.

Figure 8 is the distribution waveform of the filter coefficient Co(t) to 4T.

FIG. 9 is a schematic diagram of a combination module in a filter device according to another embodiment of the present invention.

Table 1 is an encoding table used in an embodiment of the encoding process performed by the encoder shown in FIG. 5 .

Explanation of reference numbers

10: Eight-phase PSK system 11: Gray code image module

12: 3π/8 phase rotation module 20: Filter device

13: π/16 phase rotation module 33: Weight distribution module

3: Combination module 33b: Memory unit

33a: memory 30: code table

的实部       30b：第三向量

的虚部30a: Third vector

Real part 30b of : the third vector

the imaginary part of

30c: Coded signal 34: Controller

35: Symbol designator 36: Adder controller

37: Symbol Designation Unit 60: Radio Frequency System

Detailed ways

Please refer to FIG. 3 . FIG. 3 is a schematic diagram of the filtering device 20 of the present invention and the eight-phase PSK system 10 applying the present invention. The present invention is a filtering device 20 for an eight-phase PSK system 10 . The eight-phase PSK system 10 is used to encode a series of digital bits (d _3i , d _3i+1 , d _3i+2 ) to output multiple sets of corresponding modulation signals (Ii, Qi). The eight-phase PSK system 10 includes a Gray code mapping module 11 , a 3π/8 phase rotation module 12 and a filtering device 20 .

滤波装置20是用来将该3π/8相位旋转模块12目前所产生的第二向量

进行一滤波程序，以产生一组调制信号(Ii，Qi)。该组调制信号为一基频信号，可提供予一射频系统60以产生一相对应的射频信号。The gray code mapping module 11 is used to map each triplet of digital bits into a corresponding first vector S _i through a predetermined mapping program. The 3π/8 phase rotation module 12 is used to rotate the phase of the first vector S _i currently generated by the Gray code mapping module 11 through a predetermined phase rotation procedure to generate a corresponding second vector

The filtering device 20 is used to rotate the 3π/8 phase of the second vector currently generated by the module 12

A filtering process is performed to generate a set of modulation signals (Ii, Qi). The group of modulated signals is a baseband signal, which can be provided to a radio frequency system 60 to generate a corresponding radio frequency signal.

1为π/4。Since there are only eight different permutations of the above-mentioned digital bits in groups of three, eight different digital bytes are formed, which are (1, 1, 1), (0, 1, 1), (0, 1,0), (0,0,0), (0,0,1), (1,0,1), (1,0,0), and (1,1,0). The predetermined mapping program used in the gray code mapping module 11 is to map each digital byte as having the same magnitude (magnitude) but the corresponding first vector S _i (S _i =e ^{j2πl/ 8} ), among these first vectors S _i , the phase difference between the two adjacent ones is π/4. As shown in Figure 1, the phase difference of two adjacent first vectors

1 is π/4.

第二向量 ${\hat{S}}_i({\hat{S}}_i=S_i\&CenterDot;e^{\mathrm{ji}3\mathrm{\&pi;}/8})$ 共仅有十六种可能性，且这些第二向量

之间相邻两者的相位差为π/8。如图2所示，二相邻的第二向量的相位差

为π/8。格雷码映像模块11中所使用的预定映像程序以及3π/8相位旋转模块12中所使用的相位旋转程序，是定义于GSM5.04(V8.0.8)协议中，为八相移相键控系统中的标准程序，在此不多加详述。Please refer to FIG. 2B . FIG. 2B is a phase rotation program used in the 3π/8 phase rotation module 12 shown in FIG. 1 . The predetermined phase rotation program used by the 3π/8 phase rotation module 12 is as follows: the 3π/8 phase rotation module 12 rotates the phase of the current first vector S _i each time, compared with the 3π/8 phase rotation module 12 that rotates the previous phase of the first vector S i The phase of a vector S _i is more than 3π/8 angle, thus producing the corresponding second vector

second vector ${\hat{S}}_i({\hat{S}}_i=S_i\&Center\; Dot;e^{\mathrm{the\; <figure-callout\; id="3"\; label="ji"\; filenames="C03142349E00221.png,C03142349E00231.png"\; state="\{\{state\}\}">ji</figure-callout>}3\mathrm{\&pi;}/8})$ There are only sixteen possibilities, and these second vectors

The phase difference between the adjacent two is π/8. As shown in Figure 2, the phase difference of two adjacent second vectors

is π/8. The predetermined mapping program used in the gray code mapping module 11 and the phase rotation program used in the 3π/8 phase rotation module 12 are defined in the GSM5.04 (V8.0.8) protocol, which is an eight-phase phase shift keying system The standard procedures in , will not be described in detail here.

再次旋转π/16的角度后，产生一相对应的第三向量 ${\widehat{S\&prime;}}_i({\hat{S}\&prime;}_i=\widehat{S_i}\&CenterDot;e^{\mathrm{j\&pi;}/16}).$ 权值分配模块33以多个选定的权值对于一预定的分配波形进行权重分配并储存为相对应的多个权值分配波形。该预定的分配波形可分割为多段次分配波形。权值分配模块33包含一具有多个记忆单元33b的存储器33a，而每个记忆单元33b可用来储存经过权重分配后的多个权值次分配波形。组合模块3则依据目前所产生的第三向量

，决定自权值分配模块33中要选择出哪些权值分配波形，并将所选出的权值分配波形组合起来，以产生调制信号(Ii，Qi)。As shown in FIG. 3 , the filtering device 20 includes a π/16 phase rotation module 13 , a weight distribution module 33 , and a combiner module (combiner) 3 . The π/16 phase rotation module 13 is used to convert the second vector currently produced by the 3π/8 phase rotation module 12

After rotating the angle of π/16 again, a corresponding third vector is generated ${\widehat{S\&prime;}}_i({\hat{S}\&prime;}_i=\widehat{S_i}\&Center\; Dot;e^{\mathrm{j\&pi;}/16}).$ The weight allocation module 33 performs weight allocation on a predetermined allocation waveform with multiple selected weights and stores them as corresponding multiple weight allocation waveforms. The predetermined distribution waveform can be divided into multiple distribution waveforms. The weight allocation module 33 includes a memory 33a with a plurality of memory units 33b, and each memory unit 33b can be used to store a plurality of weight sub-allocation waveforms after weight allocation. Combination module 3 is based on the third vector generated at present

, decide which weight distribution waveforms to be selected from the weight distribution module 33, and combine the selected weight distribution waveforms to generate modulation signals (Ii, Qi).

转成相对应的第三向量

以便让组合模块3处理成一定的编码信号，借着该编码信号找到适当的滤波方式。第三向量 ${\widehat{S\&prime;}}_i({\hat{S}\&prime;}_i=\widehat{S_i}\&CenterDot;e^{\mathrm{j\&pi;}/16})$ 共仅有十六种可能性，且相邻第三向量之间的相位差为π/8。如图4所示，二相邻的第三向量的相位差

为π/8。Please refer to FIG. 4 . FIG. 4 is a schematic diagram of the π/16 phase rotation module 13 shown in FIG. 3 rotating by π/16. π/16 phase rotation module 13 can convert each second vector

into the corresponding third vector

In order to allow the combination module 3 to process a certain coded signal, and find an appropriate filtering method by means of the coded signal. third vector ${\widehat{S\&prime;}}_i({\hat{S}\&prime;}_i=\widehat{S_i}\&Center\; Dot;e^{\mathrm{j\&pi;}/16})$ There are only sixteen possibilities, and the phase difference between adjacent third vectors is π/8. As shown in Figure 4, the phase difference of two adjacent third vectors

is π/8.

是由一实部与一虚部所组成。该实部是由一实部幅度与一实部符号所组成，其中该实部幅度是代表该实部的大小，该实部符号是代表该实部的正负值。该虚部是由一虚部幅度与一虚部符号所组成，其中该虚部幅度是代表该虚部的大小，该虚部符号是代表该虚部的正负值。而这些实部幅度与虚部幅度是取值于下列组合之一，该组合为cos(π/16)、cos(3π/16)、cos(5π/16)与cos(7π/16)。Every third vector

It is composed of a real part and an imaginary part. The real part is composed of a real part magnitude and a real part sign, wherein the real part magnitude represents the magnitude of the real part, and the real part sign represents the positive and negative values of the real part. The imaginary part is composed of an imaginary part amplitude and an imaginary part sign, wherein the imaginary part amplitude represents the size of the imaginary part, and the imaginary part sign represents the positive and negative values of the imaginary part. These real part magnitudes and imaginary part magnitudes are selected from one of the following combinations, which are cos(π/16), cos(3π/16), cos(5π/16) and cos(7π/16).

的相位，将该第三向量

进行一编码程序，用以产生一相对应的编码信号，所产生的编码信号将在稍后进行的该组合程序中被使用。位移缓存器32包含有多个缓存单元(未显示)，用来暂存目前以及先前编码器31所编码产生的该等编码信号。权值分配模块33亦包含于组合模块3中，而权值分配模块33所选定的该等权值是取值于下列组合之一，该组合为cos(π/16)、cos(3π/16)、cos(5π/16)与cos(7π/16)。Please refer to FIG. 5 . FIG. 5 is a schematic diagram of the combination module 3 in the filter device 20 of the present invention. The combination module 3 generates the set of modulated signals after a combination procedure according to the currently generated third vector. The combination module 3 includes an encoder 31 and a shift register 32 . Encoder 31 is based on each third vector

the phase of the third vector

An encoding process is performed to generate a corresponding encoded signal, and the generated encoded signal will be used in the combining process performed later. The shift register 32 includes a plurality of buffer units (not shown) for temporarily storing the encoded signals generated by the current and previous encoders 31 . The weight distribution module 33 is also included in the combination module 3, and the weights selected by the weight distribution module 33 are taken in one of the following combinations, the combination being cos(π/16), cos(3π/ 16), cos(5π/16) and cos(7π/16).

As shown in FIG. 5 , the combination module 3 further includes a controller 34 , a symbol designator 35 and an adder 36 . The controller 34 selects corresponding weight distribution waveforms from the weight distribution module 33 according to the real part amplitude codes temporarily stored in the buffer units. The weight distribution waveforms are formed based on multiple selected weights for the current coded signal and the previous four groups of coded signals.

The symbol designator 35 includes a plurality of symbol designating units 37 . The symbol designator 35 is under the control of the controller 34, according to the real part symbol code or the imaginary part symbol code, respectively assigns the waveforms of the weights selected by the controller 34 to specify the corresponding positive and negative symbols . The adder 36 adds up the equal weight distribution waveforms of the symbols assigned by the symbol assigner 35 to generate the group of modulation signals.

The controller 34 further selects corresponding weight distribution waveforms from the weight distribution module 33 according to the imaginary part amplitude codes temporarily stored in the buffer units. Through the control of the controller 34 , the sign designator 35 assigns corresponding positive and negative signs to the weight distribution waveforms selected by the controller 34 according to the imaginary part sign codes. Finally, the adder 36 adds up the equal weight distribution waveforms of the symbols assigned by the symbol assigner 35 to generate the imaginary part modulation signal. The modulation signal includes a real part modulation signal Ii and an imaginary part modulation signal Qi.

The filtering procedure performed by the filtering device 20 of the present invention is to multiply the current and previous predetermined number of input vectors by the predetermined distribution waveform, and finally accumulate and sum to obtain the group of modulated signals as output. There are many kinds of actual practice of the filter program. In the present invention, multiple weight distribution waveforms obtained by multiplying only 16 kinds of input vectors with the distribution waveforms given in advance are calculated in advance and stored in the memory in advance. .

Therefore, when an input vector is input to the filter device 20, the filter device 20 can directly select a group of corresponding data from the look-up table (look-up table) formed by the data prestored in the memory 33a, and then through simple accumulation and calculation and to output the set of modulated signals. Compared with the known technology, expensive multipliers originally required for multiplication can be replaced and saved. The prestored data in the memory 33a can be further simplified according to the law of trigonometric function symmetry due to the special signal processing of the present invention, and the highest can be reduced by 8 to 10 times compared with the original data to be stored. In this way, a large amount of savings can be achieved. Memory space in an eight-phase phase-shift keying system.

In addition, the π/16 phase rotation module 13 implements a special signal processing method in the filtering device 20 of the present invention. The π/16 phase rotation module 13 is used to rotate the second vector currently generated by the 3π/8 phase rotation module 12 by an angle of π/16 to generate a corresponding third vector, the purpose of which is to make different The third vector has superior symmetry, so that it can be further simplified in the future to achieve the effect of saving memory space.

Please refer to Table 1. Table 1 is the encoding table 30 used in an embodiment of the encoding process performed by the encoder 31 shown in FIG. 5 .

Table I

The encoding procedure is based on the current third vector The real part 30a and the imaginary part 30b of , and its encoded signal 30c is found from the encoding table 30 . Each of the encoded signals 30c includes a real amplitude code _Eci , a real sign code Sc _i , an imaginary amplitude code Es _i and an imaginary sign code Ss _i . In a preferred embodiment of the present invention, only 2 bits are required for the amplitude encoding of the real part and the imaginary part, and only 1 bit is required for the sign encoding of the real part and the imaginary part. That is to say, each encoded signal has 6 bits in total. According to the rules of trigonometric functions, the magnitudes of the real parts and the magnitudes of the imaginary parts corresponding to the third vectors are in one of the following combinations: cos(π/16), cos(3π/16) , cos(5π/16) and cos(7π/16). Therefore, it can be found that any amplitude of the real part and amplitude of the imaginary part in Table 1 is one of the above groups. And these four groups of real part amplitude codes _Eci are respectively cos(π/16): (00, 1), cos(3π/16): (01, 1), cos(5π/16): (10, 1) with cos(7π/16): (11, 1).

For an example illustrating the process of encoding the third vector into a corresponding encoded signal, please refer to FIG. 4 . First, a third vector numbered 12 is selected in FIG. 4 , which is equivalent to p being 12 in Table 1. Then according to a real part conversion formula cos(π(2p+1)/16) and an imaginary part conversion formula sin(π(2p+1)/16), cos(25π/16) and sin(25π/16) are obtained . However, cos(25π/16)=cos(7π/16) and sin(25π/16)=-cos(π/16) can be deduced according to the rules of trigonometric functions. Therefore, it can be obtained that the real part magnitude code _Eci is 11 (binary), the real part sign code Sc _i is 1 (binary), the imaginary part magnitude code _Esi is 00 (binary) and the imaginary part sign code _Ssi is 0 (binary), so the coded signal corresponding to the third vector numbered 12 is (11, 1, 00, 0). Wherein, when the real part sign code Sc _i or the imaginary part sign code Ss _i is 0, it represents a negative number.

Based on the GSM5.04 (V8.0.8) protocol, in the present invention, the generation of the output modulation signal is related to the current input vector and the previous input vector associated coded signals and the previous 4 groups of coded signals. For example: Ec _i-1 shown in FIG. 5 represents the real part amplitude coding of the previous group of coded signals. Therefore, the current and previous coded signals need to be temporarily stored, so that the combining module can use them in subsequent combining procedures to generate the set of modulated signals.

The weight distribution module 33 performs weight distribution on a predetermined distribution waveform with a plurality of selected weights and stores them as a plurality of corresponding weight distribution waveforms. The multiple weights selected in the weight distribution module 33 are the possible sizes of the real part and the imaginary part of all the third vectors in Table 1, which are respectively cos(π/16), cos(3π/16 ), cos(5π/16) and cos(7π/16).

Please refer to FIG. 6 , which is a schematic diagram of the predetermined allocation waveform in the filtering device 20 of FIG. 5 . According to the GSM5.04 (V8.0.8) protocol, the filter coefficient Co(t) is defined as follows:

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; for</span>}\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="T"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">T</figure-callout></span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; else</span>}\end{array}\right.$

where

and

输出的产生与目前输入向量以及先前四组输入向量有关(i＝0～4)，因此本发明的位移缓存器32中原则上暂存有包含目前以及先前四组共五组的编码信号(Ec_i，Sc_i，Es_i，Ss_i)。而分配波形也原则上分割为五段次分配波形Co_i(t)，(i＝0～4)，以分别搭配代表五个输入向量的五组编码信号。According to the GSM5.04 (V8.0.8) protocol, the output of the eight-phase phase-shift keying system (the group of modulation signals) is specified:

The generation of output is related to the current input vector and the previous four groups of input vectors (i=0～4), so in principle, the shift register 32 of the present invention temporarily stores five groups of encoded signals (Ec _i , Sc _i , Es _i , Ss _i ). In principle, the allocation waveform is divided into five segments of allocation waveform Co _i (t), (i=0˜4), so as to match five sets of coded signals representing five input vectors respectively.

The weight allocation module 33 includes a memory with five memory units 33b, and each memory unit 33b can be used to store multiple weight sub-allocation waveforms after weight allocation. For example, the memory unit shown on the far right of Fig. 3 is used to store the multiplied data of the sub-allocation waveform Co ₄ (t) and different weights: cos(π/16)*Co ₄ (t), cos (3π/16)*Co ₄ (t), cos(5π/16)*Co ₄ (t) and cos(7π/16)*Co ₄ (t). In fact, how many points need to be sampled in each section of weight sub-allocation waveform for storage depends on the actual needs of the system and the capacity of the memory unit. Generally speaking, the sampling rate of each section of weight sub-allocation waveform should be at least 16 points, it will not cause distortion.

Please refer to FIG. 7 and FIG. 8 , FIG. 7 is a distribution waveform of the filter coefficient Co(t) to 5T, and FIG. 8 is a distribution waveform of the filter coefficient Co(t) to 4T. It can be clearly seen from Fig. 7 that the first half of I and the second half of V marked on the figure are close to zero, therefore, it can be considered that these two parts can be ignored. The length of each paragraph divided based on the distribution waveform diagram is still T, therefore, after ignoring the first half of I and the second half of V shown in Figure 7, and the remaining unignored part, it is divided into 4 T paragraphs, As shown in Figure 8. In other words, since the omitted paragraphs have little effect on the filtering process, changing to use 4 memory units corresponding to the remaining un-ignored paragraphs will not only not affect the correctness of the filtering results, but also save memory usage. Wherein, the pre-stored data of the 4 memory units of the preferred embodiment of the present invention are respectively:

${\mathrm{<span\; class="notranslate">\; ROM</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

${\mathrm{<span\; class="notranslate">\; ROM</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

${\mathrm{<span\; class="notranslate">\; ROM</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 20</span>}\mathrm{<span\; class="notranslate">\; vs.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

${\mathrm{<span\; class="notranslate">\; ROM</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="C"\; filenames="C03142349E00181.png,C03142349E00231.png"\; state="\{\{state\}\}">C</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; OVS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$

Among them, the sampling rate OVS (oversampling rate) is 16 points.

Please refer to FIG. 9 . FIG. 9 is a schematic diagram of a combination module 3 in a filter device according to another embodiment of the present invention. Since the allocation waveform of the pre-existing weight allocation module 33 ( FIG. 5 ) can ignore some paragraphs, the memory units used by the weight allocation module 33 of the combination module 3 are reduced to 4 groups to achieve the effect of saving memory. Similarly, a group of modulated signals generated in the preferred embodiment of the present invention shown in FIG. 9 is only related to the current coded signal and the previous 3 groups of coded signals. Therefore, currently the filtering procedure only processes 4 sets of signals. The filtering method of the present invention will be described below based on the present implementation conditions.

As shown in Figure 9, the filter device of the present invention performs weight distribution on a predetermined distribution waveform with a plurality of selected weights in advance, so as to obtain a plurality of corresponding weight distribution waveforms, and store them in a weight Assignment module 33. Next, the encoder 31 encodes the data provided by the encoding table in Table 1 to generate an encoded signal (Ec _i , Sc _i , Es _i , Ss _i ) corresponding to the third vector generated above. Each coded signal includes a real amplitude code _Eci , a real sign code Sc _i , an imaginary amplitude code Es _i and an imaginary sign code Ss _i . Then, the encoded signals (Ec _i , Sci _, Es _i , Ss _i ) encoded by the encoder 31 at present and previously are temporarily stored in the shift register 32 . Then, according to the temporarily stored real-part amplitude codes _Eci or imaginary-part amplitude codes Es _i , corresponding weight distribution waveforms are respectively selected from the weight distribution module 33 . Then, according to the real part symbol code Sc _i or the imaginary part symbol code _{Ss i of} the aforementioned coded signals (Eci _{, Sci} , _Esi , Ssi) with the symbol designator 35, the selected equal weight The value assignment waveform specifies the corresponding positive and negative signs. Finally, the selected weight distribution waveforms are combined by the adder 36 to generate modulation signals (Ii, Qi) including real part modulation signals and imaginary part modulation signals.

Through the above detailed description of the preferred embodiments, it is hoped that the characteristics and spirit of the present invention can be described more clearly, and the scope of the present invention is not limited by the preferred embodiments disclosed above. On the contrary, the intention is to cover various changes and equivalent arrangements within the scope of the appended claims of the present invention. Therefore, the scope of the claims for the application of the present invention should be interpreted in the broadest way based on the above description, so as to cover all possible changes and equivalent arrangements.

Claims (24)

1. filter that is used for one or eight phase phase-shift keying (8PSK) systems, this eight phases phase shift keyed system is to be used for a series of digit order number is encoded, to export the corresponding modulation signals of many groups, this eight phases phase shift keyed system comprises:

One Gray code image module, being used for every ternary digit order number is a corresponding primary vector through a predetermined map program reflection;

One 3 π/8 phase place rotary modules are used for phase place with the present primary vector that produces of this Gray code image module, are rotated through a predetermined phase place rotation program, to produce a corresponding secondary vector; And

One filter is used for this 3 π/present secondary vector that produces of 8 phase place rotary modules is carried out filtering, to produce one group of corresponding modulation signal in these many groups;

This filter comprises in addition:

One π/16 phase place rotary modules is used for this 3 π/present secondary vector that produces of 8 phase place rotary modules is rotated the angle of π/16 once more, to produce corresponding the 3rd vector;

One weights distribution module carries out weight allocation for a predetermined distribution waveform and saves as corresponding a plurality of weights distributing waveform with a plurality of selected weights; And

One composite module, according to present the 3rd vector that produces, which weights decision will select in this weights distribution module distributes waveform, and distributes waveform combination to get up selected weights, to produce this group modulation signal.

2. filter as claimed in claim 1, wherein above-mentioned every ternary digit order number has eight kinds of different arrangements, therefore form eight kinds of different digital bytes, map program that should be predetermined is as follows: but with the corresponding primary vector of each digital byte reflection for having the same magnitude out of phase, adjacent both phase difference is π/4 between these primary vectors.

3. filter as claimed in claim 1, wherein phase place rotation program that should be predetermined is as follows: the phase place of the primary vector that the each rotation of this 3 π/8 phase place rotary modules is present, be the angle of rotating many 3 π of phase place/8 of previous primary vector than this 3 π/8 phase place rotary modules, therefore produce this corresponding secondary vector.

4. filter as claimed in claim 2 wherein only has 16 kinds of possibilities altogether through this 3 π/8 phase place rotary modules rotate these a plurality of secondary vectors that produce, and adjacent both phase difference is π/8 between these secondary vectors.

5. filter as claimed in claim 1, wherein through this π/16 phase place rotary modules rotate produce should be a plurality of the 3rd vectorially common 16 kinds of possibilities be only arranged, and adjacent both phase difference is π/8 between this grade in an imperial examination three-dimensional amount.

6. filter as claimed in claim 5, wherein each this grade in an imperial examination three-dimensional amount is made up of a real part and an imaginary part, this real part is made up of a real part amplitude and a real part of symbol, and this real part amplitude is to represent the size of this real part, and this real part of symbol is to represent the positive negative value of this real part; And this imaginary part is made up of an imaginary part amplitude and an imaginary part of symbol, and this imaginary part amplitude is to represent the size of this imaginary part, and this imaginary part of symbol is a positive negative value of representing this imaginary part.

7. filter as claimed in claim 6, wherein corresponding these real part amplitudes of all these grade in an imperial examination three-dimensional amounts and these imaginary part amplitudes be value in one of following combination, this is combined as: cos (π/16), cos (3 π/16), cos (5 π/16) and cos (7 π/16).

8. filter as claimed in claim 1, wherein this weights distribution module is to be contained in this composite module, and these selected weights of this weights distribution module be value in one of following combination, this is combined as: cos (π/16), cos (3 π/16), cos (5 π/16) and cos (7 π/16).

9. filter as claimed in claim 8, wherein these selected weights are to derive all these grade in an imperial examination three-dimensional amounts via the trigonometric function rule in this weights distribution module.

10. filter as claimed in claim 1, wherein this composite module comprises in addition:

One encoder is encoded the 3rd vector to produce a corresponding code signal with the phase place according to each the 3rd vector; And

One bit shift register includes a plurality of buffer units, is used for keeping at present and these code signals of the coded generation of this encoder before.

11. filter as claimed in claim 10, wherein each these code signal comprises a real part amplitude coding, real part of symbol coding and an imaginary part amplitude coding and imaginary part of symbol coding.

12. filter as claimed in claim 11, wherein this group modulation signal comprises a real part modulation signal and an imaginary part modulation signal.

13. filter as claimed in claim 12, wherein this composite module comprises in addition:

One controller with according to these real part amplitude codings of being kept in these buffer units, distributes waveform and select corresponding weights respectively in this weights distribution module;

One symbol is specified device, under the control via this controller, with according to these reals part of symbol codings, distributes waveforms to specify corresponding sign symbol selected these weights that go out of this controller respectively; And

One adds up device, is used for specifying these weights of the specified intact symbol of device to distribute waveform adder this symbol, to produce this real part modulation signal.

14. filter as claimed in claim 13, wherein this controller distributes waveform in addition according to these imaginary part amplitude codings of being kept in these buffer units and select corresponding weights respectively in this weights distribution module; And under the control via this controller, specify device according to these imaginary parts of symbol codings by this symbol, distribute waveforms to specify corresponding sign symbol selected these weights that go out of this controller respectively; Specify these weights of the specified intact symbol of device to distribute waveform adder to get up this symbol by this totalling device more at last, to produce this imaginary part modulation signal.

15. filter as claimed in claim 13, wherein this symbol specifies device to include a plurality of symbol designating unit, each this symbol designating unit is according to this real part of symbol coding and this imaginary part of symbol coding, the sign symbol of coming selected these weights of this controller of corresponding appointment to distribute waveform.

16. filter as claimed in claim 11, wherein this code signal has 6 altogether, and this real part amplitude coding is 2, and this real part of symbol is encoded to 1, and this imaginary part amplitude coding is 2, and this imaginary part of symbol is encoded to 1.

17. filter as claimed in claim 1, wherein should may be partitioned into multistage sub-distribution waveform by predetermined distribution waveform, this weights distribution module then comprises a memory with a plurality of mnemons, and each mnemon can be used to store a plurality of weights sub-distribution waveforms through after the weight allocation.

18. filter as claimed in claim 1, wherein this group modulation signal is a fundamental frequency signal, can provide to give a radio system to produce a corresponding radio frequency signal.

19. a filtering method that is used for one or eight phase phase-shift keying (8PSK) systems, this eight phases phase shift keyed system is to be used for a series of digit order number is encoded, and to export the corresponding modulation signal of many groups, this eight phases phase shift keyed system comprises:

One Gray code image module, being used for every ternary digit order number is a corresponding primary vector through a predetermined map program reflection;

One 3 π/8 phase place rotary modules are used for phase place with the present primary vector that produces of this Gray code image module, are rotated through a predetermined phase place rotation program, to produce a corresponding secondary vector; And

One filter is used for this 3 π/present secondary vector that produces of 8 phase place rotary modules is carried out filtering, to produce one group of corresponding modulation signal in these many groups;

This filtering method comprises:

With this 3 π/present secondary vector that produces of 8 phase place rotary modules, rotate the angle of π/16 once more, to produce corresponding the 3rd vector;

Carry out weight allocation with a plurality of selected weights for a predetermined distribution waveform, distribute waveform to draw corresponding a plurality of weights, and be stored in the weights distribution module; And

According to present the 3rd vector that produces, decision to select above-mentioned in which weights distribute waveform, and weights that will be selected distribution waveform combination gets up, to produce this group modulation signal.

20. filtering method as claimed in claim 19, wherein this filtering method comprises in addition:

Phase place according to each the 3rd vector encodes the 3rd vector to produce a corresponding code signal; And

Temporary at present and these code signals of the coded generation of this encoder before.

21. filtering method as claimed in claim 20, wherein each these code signal comprises a real part amplitude coding, real part of symbol coding and an imaginary part amplitude coding and imaginary part of symbol coding.

22. filtering method as claimed in claim 21, wherein this group modulation signal comprises a real part modulation signal and an imaginary part modulation signal.

23. filtering method as claimed in claim 22, wherein this filtering method comprises in addition:

According to these real part amplitude codings of being kept in, distribute waveform and in this weights distribution module, select corresponding weights respectively;

According to these reals part of symbol coding, these weights distribution waveforms that respectively will be selected go out are specified corresponding sign symbol; And

Distribute waveform adder to get up these weights of specified intact symbol, to produce this real part modulation signal.

24. filtering method as claimed in claim 23, wherein this filtering method comprises in addition:

According to these imaginary part amplitude codings of being kept in, distribute waveform and in this weights distribution module, select corresponding weights respectively;

According to these imaginary parts of symbol coding, these weights distribution waveforms that respectively will be selected go out are specified corresponding sign symbol; And

Distribute waveform adder to get up these weights of specified intact symbol, to produce this imaginary part modulation signal.

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