CN107528543B - Efficient frequency sweeping signal generation method matched with FFT (fast Fourier transform) processing - Google Patents
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Abstract
The invention discloses a high-efficiency frequency sweeping signal generation method matched with FFT (fast Fourier transform) processing, and belongs to the technical field of radio frequency network analysis. The method comprises the steps of generating and storing the waveform data of the high-efficiency frequency sweeping signal matched with the FFT processing of the receiving channel, counting according to the sampling rate of the FFT analysis, synchronously reading the stored waveform, converting the sampling rate, carrying out digital frequency conversion, carrying out analog-to-digital conversion, carrying out analog up-conversion and the like, and realizes the high-efficiency generation of the frequency sweeping signal. The invention has the advantages of high efficiency, high response speed, high integration degree, simple realization and the like when the FFT is used for network analysis, and is an important improvement on the prior art.
Description
Technical Field
The invention relates to the technical field of frequency sweep signal generation and digital network analysis, in particular to a high-efficiency frequency sweep signal generation method matched with FFT (fast Fourier transform) processing.
Background
In the prior art, frequency sweep output of most network analysis devices and channel calibration of devices such as a frequency spectrograph and the like use signals with a single frequency to perform frequency scanning, and each time, a signal with a single frequency is generated.
Therefore, the processing capability of the signal receiving end cannot be fully utilized due to the fact that the sweep frequency signal generated by the signal output end is not matched with the processing capability of the signal receiving end, and the sweep frequency signal is a serious waste of the signal processing capability.
Disclosure of Invention
In view of the above, the present invention is directed to a method for generating a frequency sweep signal with high efficiency by matching FFT processing, which is capable of adapting to the signal processing capability of a receiving end based on FFT analysis, accelerating the frequency sweep rate of a device, and significantly improving the performance of instruments such as a spectrum analyzer and a frequency sweep generator.
Based on the above purpose, the technical scheme provided by the invention is as follows:
a high-efficiency frequency sweep signal generation method matched with FFT processing is applied to a frequency sweep signal generation device and used for matching the signal processing capacity of a receiving end, and the receiving end sequentially carries out analog down conversion, A/D conversion, orthogonal processing of digital zero intermediate frequency, sampling rate conversion and 2NThe FFT processing of the point, the high-efficient sweep frequency signal generating method includes the following steps:
(1) generation 2 by a sweep control Unit according to specific sweep Signal requirementsNWaveform data of the point, the waveform data is matched with FFT processing of a receiving end, wherein N is a natural number;
(2) 2 to be generated by a sweep control UnitNLoading the waveform data of the points into a waveform storage module, then finishing the initialization of the sweep frequency signal generating device, and controlling the sweep frequency signal generating device to enter a sweep frequency signal generating mode;
(3) with a clock signal F at the same frequency as the input data sample frequency of the FFT processing at the receiving endc1A driving cyclic address generation module;
(4) the cyclic address generation module generates clock signal Fc1Generating an N-bit count output of plus 1 per clock, and when the count reaches 2N-1 and then changing the count value to zero when the next clock signal arrives, thus continuously counting cycles, each cycle generating 2NUsing the continuous counting value as an address to read the data in the waveform storage module;
(5) at clock signal Fc1Synchronously reading a sweep frequency waveform signal from the waveform storage module under the control of an N-bit address;
(6) performing multi-stage serial sampling rate interpolation conversion on the read sweep frequency waveform signal to ensure that the sampling rate of the sweep frequency waveform signal is the same as the sampling rate of digital frequency conversion;
(7) the sweep frequency waveform signal after the sampling rate interpolation conversion is converted into a complex digital intermediate frequency signal through digital complex frequency conversion, and then the complex digital intermediate frequency signal is converted into two paths of analog orthogonal intermediate frequency signals through high-speed digital-to-analog conversion;
(8) two paths of simulated orthogonal intermediate frequency sweep signals are changed into radio frequency output signals meeting the frequency and amplitude requirements through an up-converter;
(9) the sweep frequency control unit generates and loads waveform data of the sweep frequency signal, calculates and distributes control parameters of each module according to the central frequency, bandwidth, amplitude and phase requirements of the sweep frequency signal, and controls the function completion of the whole sweep frequency device.
Optionally, the specific manner of generating the waveform data in step (1) is as follows:
a. if the amplitudes of the sub-signals contained in the waveform data are different and the initial phases are all zero, generating 2 by using the formula (1)NWaveform data in dot complex form:
b. if the amplitudes of the sub-signals included in the waveform data are not the same but are symmetrical about the center frequency and the initial phases are all zero, then 2 is generated using equation (2) or equation (3)NReal waveform data of points:
c. if the amplitude of the sub-signals included in the waveform data is the same and the initial phases are all zero, then 2 is generated using equation (4) or equation (5)NReal waveform data of points:
in the formulas (1) - (5), f (k) is a sweep frequency signal synthesized by 2(m + r) +1 sub-signals with different frequencies, wherein k is the sampling time of the current waveform data, and the value range of k is 0-2N-an integer of 1; m is an integer value of a spectral line corresponding to the highest frequency point of the effective bandwidth processed by the FFT; r is a margin value taken for adapting to different window functions added by FFT processing, and r is an integer between 3 and 6; a isnAnd bnRespectively the amplitude of the same phase path and the amplitude of the orthogonal path of the nth sub-signal of the sweep frequency signal; j is an imaginary unit.
As can be seen from the above description, the beneficial effects of the present invention are:
1. the invention can realize the sweep frequency signal matched with the signal processing capability of the FFT processing of the receiving end, thereby enabling the signal processing of all frequency points in the effective bandwidth to be completed by one FFT processing of the receiving end, and compared with the traditional single-signal sweep frequency type realization scheme, the processing efficiency of the whole signal generating-signal receiving system is improved by 2m times.
2. The invention can use high-speed NCO (numerically controlled oscillator) and high-speed D/A conversion chip, so that the digital frequency conversion can realize intermediate frequency (-f)s,fsHigh speed sweep frequency (f) in rangesRepresenting the highest center frequency that digital frequency conversion can achieve), thereby simplifying the design of the analog up-converter;
3. the invention can adopt high-speed FPGA (field programmable gate array) and high-speed digital chip as hardware basis, and the device manufactured by the principle has the advantages of high integration degree, small volume, simple structure, high reliability, easy upgrading and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of a method for efficient frequency sweep signal generation in an embodiment of the present invention;
FIG. 2 is an embodiment of the present inventionThe amplitude spectrogram of the efficient frequency sweeping signal matched with the FFT processing in the example; in the context of figure 2 of the drawings,the amplitude of the spectral line corresponding to the nth point is shown, the spectral line corresponding to the effective bandwidth of FFT analysis is-m, and a redundant sub-signal with r being 3 is taken in order to adapt to the barrier effect and the added window function;
FIG. 3 is a schematic diagram of an implementation of a sample rate interpolation transform and digital frequency conversion portion in an embodiment of the present invention; in fig. 3, if the waveform data is complex, two paths of interpolation transformations with the same sampling rate are required; if the waveform data is a real number, only one path of sampling rate interpolation transformation is needed;
fig. 4 is a functional block diagram of a hardware implementation of an embodiment of the present invention. In fig. 4, if only the frequency sweep signal needs to be generated, the DDR RAM is not needed in general, and the waveform data can be stored only by using the RAM inside the FPGA.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings in conjunction with specific embodiments.
A high-efficiency frequency sweep signal generation method matched with FFT processing is applied to a frequency sweep signal generation device and used for matching the signal processing capacity of a receiving end, and the receiving end sequentially carries out analog down conversion, A/D conversion, orthogonal processing of digital zero intermediate frequency, sampling rate conversion and 2NThe FFT processing of the point, the high-efficient sweep frequency signal generating method includes the following steps:
(1) generation 2 by a sweep control Unit according to specific sweep Signal requirementsNWaveform data of the point, the waveform data is matched with FFT processing of a receiving end, wherein N is a natural number;
(2) 2 to be generated by a sweep control UnitNLoading the waveform data of the points into a waveform storage module, then finishing the initialization of the sweep frequency signal generating device, and controlling the sweep frequency signal generating device to enter a sweep frequency signal generating mode;
(3) to and withReceiving end FFT processed input data sampling frequency identical clock signal Fc1A driving cyclic address generation module;
(4) the cyclic address generation module generates clock signal Fc1Generating an N-bit count output of plus 1 per clock, and when the count reaches 2N-1 and then changing the count value to zero when the next clock signal arrives, thus continuously counting cycles, each cycle generating 2NUsing the continuous counting value as an address to read the data in the waveform storage module;
(5) at clock signal Fc1Synchronously reading a sweep frequency waveform signal from the waveform storage module under the control of an N-bit address;
(6) performing multi-stage serial sampling rate interpolation conversion on the read sweep frequency waveform signal to ensure that the sampling rate of the sweep frequency waveform signal is the same as the sampling rate of digital frequency conversion;
(7) the sweep frequency waveform signal after the sampling rate interpolation conversion is converted into a complex digital intermediate frequency signal through digital complex frequency conversion, and then the complex digital intermediate frequency signal is converted into two paths of analog orthogonal intermediate frequency signals through high-speed digital-to-analog conversion; by varying the frequency of a Numerically Controlled Oscillator (NCO) within a digital frequency converter, [ -f ] can be achieveds,fsHighly efficient frequency sweep of arbitrary center frequencies in the range, where fsIs the highest center frequency that can be achieved by digital frequency conversion;
(8) two paths of simulated orthogonal intermediate frequency sweep signals are changed into radio frequency output signals meeting the frequency and amplitude requirements through an up-converter;
(9) the sweep frequency control unit generates and loads waveform data of the sweep frequency signal, calculates and distributes control parameters of each module according to the central frequency, bandwidth, amplitude and phase requirements of the sweep frequency signal, and controls the function completion of the whole sweep frequency device.
Optionally, the specific manner of generating the waveform data in step (1) is as follows:
a. if the amplitudes of the sub-signals contained in the waveform data are different and the initial phases are all zero, generating 2 by using the formula (1)NWaveform data in dot complex form:
b. if the amplitudes of the sub-signals included in the waveform data are not the same but are symmetrical about the center frequency and the initial phases are all zero, then 2 is generated using equation (2) or equation (3)NReal waveform data of points:
c. if the amplitude of the sub-signals included in the waveform data is the same and the initial phases are all zero, then 2 is generated using equation (4) or equation (5)NReal waveform data of points:
in the formulas (1) - (5), f (k) is a sweep frequency signal synthesized by 2(m + r) +1 sub-signals with different frequencies, wherein k is the sampling time of the current waveform data, and the value range of k is 0-2N-an integer of 1; m is an integer value of a spectral line corresponding to the highest frequency point of the effective bandwidth processed by the FFT; r is a margin value taken for adapting to different window functions added by FFT processing, and r is an integer between 3 and 6; a isnAnd bnRespectively the amplitude of the in-phase path and the amplitude of the orthogonal path of the nth sub-signal of the sweep frequency signal; j is an imaginary unit. It can be seen that the data output generated by equation (1) is a complex form of swept waveform, and the data output generated by equations (2) to (5) is a real form of swept waveform; meanwhile, in the step (6), two paths of synchronous and completely same sampling rate interpolation transformation are needed for the frequency sweeping waveform in the complex form, and only one path of sampling rate interpolation transformation is needed for the frequency sweeping waveform in the real form; in addition, design an、bnThe relation with n can obtain sweep frequency signals with different characteristics.
Fig. 1 is a schematic diagram of a frequency sweep signal generation method, in which a dashed box represents a signal receiving end, and it is assumed that a signal processing procedure of a receiving processing channel sequentially includes: 1. converting the frequency of the received radio frequency signal to an appropriate central frequency through an analog down converter and adjusting the frequency to an appropriate amplitude, 2, converting the radio frequency signal to a digital signal through high-speed A/D (analog to digital) conversion, 3, converting the digital signal to a zero intermediate frequency complex signal through a digital down converter, and 4, converting the complex signal to an appropriate sampling rate F through sampling rate conversionc1Sample rate F, 5c1After being processed by windowing function, the complex signal is processed by 2NAnd (6) FTT processing of points, and performing subsequent processing on parameters such as amplitude, phase and time delay on the FTT processing result.
The method can be realized based on a high-speed D/A chip and an FPGA chip, and the hardware composition of the method is shown in figure 4. According to the signal processing procedure of the receiving channel, a corresponding efficient frequency sweeping signal generation method is shown in fig. 1, and comprises the following steps:
(1) firstly, the sweep frequency control unit selects a formula according to the requirement of a specific sweep frequency signal, and generates 2 by using the selected formulaNWaveform data of the point, the waveform data being matched to FFT processing of the receive channel, where N is a natural number; a schematic diagram of the magnitude spectrum of the generated waveform data is shown in fig. 2.
Specifically, when the amplitudes of the sub-signals included in the waveform data are different and the initial phases are all zero, 2 is generated using equation (1)NWaveform data in dot complex form:
when the amplitudes of the sub-signals included in the waveform data are not the same but are symmetrical with respect to the center frequency and the initial phases are all zero, 2 is generated using formula (2) or formula (3)NReal waveform data of points:
the amount of data generated by the formula (2) or the formula (3) is only half of the amount of data of the formula (1), and is suitable for generating sub-signal coefficients capable of compensating for the amplitude-frequency characteristic of the digital transmission section, such as a CIC filter for compensating a channel, the output of a D/a, and the like.
When the amplitude of the sub-signals included in the waveform data is the same and the initial phases are all zero, 2 is generated using formula (4) or formula (5)NReal waveform data of points:
the calculation of formula (4) or formula (5) is relatively simple, and the generated data is only half of the data of formula (1), so that the equipment for taking other calibration measures for the transmission channel can be used. The data generated by equation (4) or equation (5) is independent of the transmission characteristics of the channel, so that the same waveform data can be used by the FFT receiving the same number of points.
In the above formula, f (k) is a sweep frequency signal synthesized by 2(m + r) +1 sub-signals with different frequencies, where k is the sampling time of the current waveform data, and the value range of k is 0-2N-an integer of 1; m is an integer value of a spectral line corresponding to the highest frequency point of the effective bandwidth processed by the FFT; r is a margin value taken for adapting to different window functions added during FFT processing, and is an integer between 3 and 6; a isnAnd bnRespectively, the amplitude of the in-phase path and the amplitude of the orthogonal path of the nth sub-signal of the sweep frequency signal can be a performed according to the amplitude-frequency and phase-frequency characteristics of the sweep frequency signal generating channel and the receiving channeln、bnThe transmission characteristics of the analog filters of the transmission channel are asymmetrical with respect to the center frequency, resulting in an、bnAnd a-n、b-nNot equal;
as can be seen from equations (1) to (5), the minimum common period of all the sub-signals is k 2NAnd the normalization is completed, the shaping data storage can be carried out; the data with the minimum common period is stored and cyclically read in the waveform storage module, so that a sweep frequency signal with any length can be formed; at lower FFT analysis point (< 2)18) Directly using a block RAM inside the FPGA; if the waveform storage of an ultra-long period is required, an external DDR RAM is required.
(2) Sweep control Unit 2 to be generatedNAnd loading the waveform data of the points into a waveform storage module, then finishing the initialization of the sweep frequency signal generation device, and controlling the whole device to enter a sweep frequency signal generation mode.
(3) Sampling clock signal F of input data using FFT processing of reception channelc1Driving a cyclic address generation module or generating a clock signal F having the same frequency as the sampling clock frequency of the FFT input data by using a clock generation circuitc1The cyclic address generation module is driven.
In a usual instrument device such as a scalar network analyzer, a vector network analyzer, a sweep generator, a spectrometer, or the like, a generation section of a sweep signal and a reception channel section are in one device case, so that a sampling clock signal F of input data for FFT processing of the reception channel is receivedc1May be provided directly to the cyclic address generation module.
(4) Cyclic address generating module pair clock signal Fc1Generating an N-bit count output of 1 per clock, up to 2NAfter-1, the count value is changed to zero when the next clock arrives, and the count operation of adding 1 per clock is carried out, so that the counting is continuously circulated, and each circulation generates 2NThe successive count values are used as addresses to read the waveform memory block.
(5) At clock Fc1Under the control of N-bit address, synchronously reading out sweep waveform signals from the waveform storage module, wherein the data output generated by formula (1) is complex sweep waveform, and the data output generated by formulas (2) to (5) are dataThe output is a real swept waveform.
The sampling frequency of the read-out waveform data is the same as that of the FFT of the receiving channel, the highest sampling frequency of the FFT depends on the clock frequency of the FFT (about 250MHz) that the FPGA can implement, and the lowest clock frequency of the FFT depends on the resolution requirement (on the order of about 100 Hz) of the receiving channel.
(6) And performing multi-stage serial sampling rate conversion on the read frequency sweeping signals to ensure that the sampling rate of the frequency sweeping signals is the same as that of digital frequency conversion, wherein two synchronous identical sampling rate interpolation conversions are required for the frequency sweeping waveforms in a complex form, and only one sampling rate interpolation conversion is required for the frequency sweeping waveforms in a real number.
The specific implementation of this step is shown in FIG. 3, where the D/A and digital frequency converter use fixed high-speed sampling rate, which is favorable for the overall index design of the device, the sampling frequency of the digital frequency converter using DAC5688 is fixed at 800MHz, the sampling rate of the 100 Hz-250 MHz sampling frequency must be converted into 800MHz by interpolation, and a filter for resisting image interference must be used, since the interpolation multiple of the sampling frequency is from 3.2 times to 8 × 10 times6The interpolation filters are difficult to realize by one interpolation filter, so that the interpolation filters which are connected in series in multiple poles are adopted, wherein the interpolation filter of the first stage adopts a FARROW structure to realize decimal interpolation of 1-2 times, and the filters of the subsequent interpolation stages can use CIC filters of four stages to five stages and polyphase filters to realize interpolation of 1-2 times20Multiple interpolation, one stage of which realizes 16 times interpolation, and the other stages realize 32 times or 64 times interpolation, and each stage can be selectively connected or bypassed according to the total interpolation multiple. And finally, 2-time, 4-time and 8-time interpolation selection is realized by adopting a half-band interpolation filter in the DAC 5688.
(7) The sweep frequency signal after sampling rate conversion is converted into a complex digital intermediate frequency signal through digital frequency conversion, and then the complex digital intermediate frequency signal is converted into two paths of analog orthogonal intermediate frequency signals through high-speed D/A; by varying the frequency of a Numerically Controlled Oscillator (NCO) within a digital frequency converter, [ -f ] can be achieveds,fsHighly efficient frequency sweep of arbitrary center frequencies in the range, where fsIs the highest center frequency that can be achieved by digital frequency conversion.
As shown in fig. 3, the specific implementation manner of this step is that the clock frequency of the NCO inside the DAC5688 is set to 800MHz, the achievable output frequency is (-300 MHz,300 MHz), and the frequency range of the digital quadrature intermediate frequency signal obtained by complex mixing with the waveform data is also (-300 MHz,300 MHz); the wide digital intermediate frequency range enables the local oscillator design of the analog up-converter to avoid considering small frequency stepping, and simplifies the local oscillator design of the up-converter; after the digital orthogonal intermediate frequency signal is subjected to synchronous double-path D/A conversion, the digital orthogonal intermediate frequency signal is converted into an analog orthogonal intermediate frequency signal and is output to a single-sideband up-converter chip, and the design difficulty of a subsequent filter can be reduced.
(8) The simulated intermediate frequency sweep frequency signal is changed into a radio frequency output signal meeting the frequency and amplitude requirements after passing through an up-converter.
Frequency sweep in the FFT range is generated from the waveform data, frequency sweep in the (-300 MHz,300 MHz) range (which is the maximum range when using a DAC5688 chip) is done by digital frequency conversion, spectrum shifting is done using an up-converter and frequency sweep in a larger frequency range is done.
(9) The sweep frequency control unit generates and loads waveform data of the sweep frequency signal, calculates and distributes control parameters of each module according to the requirements of the center frequency, the bandwidth, the amplitude, the phase and the like of the sweep frequency signal, and controls the function completion of the whole sweep frequency device.
The frequency sweep control unit can use a DSP chip or an ARM processor as a hardware core and is used for calculating waveform data according to the number of points of FFT of a receiving channel, effective bandwidth, amplitude-phase requirements of a transmission channel and the like, loading the waveform data to an FPGA during initialization, selecting interpolation multiples of cascaded interpolation filters according to sampling frequency of the FFT, controlling central frequency of an NCO and central frequency of an analog up-converter according to frequency sweep frequency, and the like, and finishing the control function of frequency sweep generation and the communication function of an upper module.
In the above example, the frequency interval of the sub-signal is taken as one spectral line of the FFT, but it is obvious that other integer multiples of p of the spectral line interval may be used, and it is only necessary to change n in the equations (1) to (5) to np and simply replace it.
In addition, the implementation principle and hardware of the invention can also be popularized and applied to the generation of other periodic signals, provided that the waveform memory can store waveform data of one period of the signal to be output.
In summary, the invention has the advantages of high efficiency, fast response speed, high integration degree, simple realization and the like when the FFT is used for network analysis, and is an important improvement on the prior art.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples. Any omissions, modifications, substitutions, improvements and the like in the foregoing embodiments are intended to be included within the scope of the present invention within the spirit and principle of the present invention.
Claims (1)
1. A high-efficiency frequency sweeping signal generation method matched with FFT processing is characterized by being applied to a frequency sweeping signal generation device and used for matching the signal processing capacity of a receiving end, and the receiving end sequentially carries out analog down conversion, A/D conversion, orthogonal processing of digital zero intermediate frequency, sampling rate conversion and 2NThe FFT processing of the point, the high-efficient sweep frequency signal generating method includes the following steps:
(1) generation 2 by a sweep control Unit according to specific sweep Signal requirementsNWaveform data of the point, the waveform data is matched with FFT processing of a receiving end, wherein N is a natural number;
(2) 2 to be generated by a sweep control UnitNLoading the waveform data of the points into a waveform storage module, then finishing the initialization of the sweep frequency signal generating device, and controlling the sweep frequency signal generating device to enter a sweep frequency signal generating mode;
(3) with a clock signal F at the same frequency as the input data sample frequency of the FFT processing at the receiving endc1A driving cyclic address generation module;
(4) the cyclic address generation module generates clock signal Fc1Generating an N-bit count output of plus 1 per clock, and when the count reaches 2NAfter 1 at the nextThe clock signal reaches and changes the counting value to zero, thus continuously and circularly counting, each cycle generates 2NUsing the continuous counting value as an address to read the data in the waveform storage module;
(5) at clock signal Fc1Synchronously reading a sweep frequency waveform signal from the waveform storage module under the control of an N-bit address;
(6) performing multi-stage serial sampling rate interpolation conversion on the read sweep frequency waveform signal to ensure that the sampling rate of the sweep frequency waveform signal is the same as the sampling rate of digital frequency conversion;
(7) the frequency of a digital control oscillator in the digital frequency conversion is changed, the sweep frequency waveform signal after sampling rate interpolation conversion is subjected to digital complex frequency conversion to be converted into a complex digital intermediate frequency signal, and then the complex digital intermediate frequency signal is converted into two paths of analog orthogonal intermediate frequency signals by high-speed digital-to-analog conversion;
(8) two paths of simulated orthogonal intermediate frequency sweep signals are changed into radio frequency output signals meeting the frequency and amplitude requirements through an up-converter;
(9) the sweep frequency control unit generates and loads waveform data of the sweep frequency signal, calculates and distributes control parameters of each module according to the central frequency, bandwidth, amplitude and phase requirements of the sweep frequency signal, and controls the function completion of the whole sweep frequency device;
the specific mode for generating the waveform data in the step (1) is as follows:
a. if the amplitudes of the sub-signals contained in the waveform data are different and the initial phases are all zero, generating 2 by using the formula (1)NWaveform data in dot complex form:
b. if the amplitudes of the sub-signals included in the waveform data are not the same but are symmetrical about the center frequency and the initial phases are all zero, then 2 is generated using equation (2) or equation (3)NReal waveform data of points:
c. if the amplitude of the sub-signals included in the waveform data is the same and the initial phases are all zero, then 2 is generated using equation (4) or equation (5)NReal waveform data of points:
in the formulas (1) - (5), f (k) is a sweep frequency signal synthesized by 2(m + r) +1 sub-signals with different frequencies, wherein k is the sampling time of the current waveform data, and the value range of k is 0-2N-an integer of 1; m is an integer value of a spectral line corresponding to the highest frequency point of the effective bandwidth processed by the FFT; r is a margin value taken for adapting to different window functions added by FFT processing, and r is an integer between 3 and 6; a isnAnd bnRespectively the amplitude of the same phase path and the amplitude of the orthogonal path of the nth sub-signal of the sweep frequency signal; j is an imaginary unit.
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