CN111835314B - Anti-interference extractor for extracting 1-2 times of any multiple and design method thereof - Google Patents
Anti-interference extractor for extracting 1-2 times of any multiple and design method thereof Download PDFInfo
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Abstract
An anti-interference extractor for extracting 1-2 times of any multiple and a design method thereof. An anti-interference decimator comprising an anti-aliasing low pass filter and a polynomial interpolation filter; the design method comprises the following steps: determining passband cut-off frequencies of the anti-aliasing low pass filter and the polynomial interpolation filter; determining a stop band cut-off frequency of the anti-aliasing low pass filter and a first stop band frequency range of the polynomial interpolation filter; determining the number and the order of polynomials used by a polynomial interpolation filter; calculating coefficients of an anti-aliasing low-pass filter and a polynomial interpolation filter; calculating the amplitude-frequency response of the anti-interference extractor; judging whether the amplitude-frequency response reaches a preset interference suppression level threshold value in an interference frequency band or not: if not, re-executing the steps; if so, the anti-interference extractor is successfully designed. The anti-interference extractor designed by the method has simple structure, is convenient to realize and can effectively inhibit interference.
Description
Technical Field
The invention relates to the field of digital signal processing, in particular to multi-rate signal processing, in particular to an anti-interference extractor for extracting any multiple between 1-2 times and a design method thereof.
Background
Digital Down Converters (DDCs) are an important component of all-digital communication receivers. It is typically composed of a cascaded integrator-comb filter (CIC) for performing large integer-multiple decimation, a plurality of half-band decimators for performing 2-fold decimation, and a polynomial interpolation filter for performing 1-2-fold decimation.
The polynomial interpolation filter is usually implemented by using a classical Farrow filter structure, as shown in fig. 1 and 2.
However, it is disadvantageous to implement 1-2 times decimation using only one polynomial interpolation filter: after extractionAn interference signal in a specific frequency band is mixed into the frequency band of the baseband signal, and interference is caused. Specifically, as shown in fig. 3, the bandwidths of the signals involved are normalized bandwidths, the bandwidth of the baseband signal before extraction is assumed to be B, and the bandwidth distribution of the baseband signal is [ -B, B]The extraction multiple of the polynomial interpolation filter is x, x is E [1, 2]]. According to the multi-rate signal processing theory, the bandwidth of the baseband signal is widened to xB after x times extraction, so that the frequency band distribution range is widened to [ -xB, xB]. Since the extraction of the signals by the polynomial interpolation filter is realized by resampling, it is known from the sampling theorem that the frequency bands [1-xB,1+xB ] after resampling the signals]The signals within (if present) may be mixed into the band range of the baseband signal, causing interference. And band [1-xB,1+xB ]]The signal in is exactly the frequency band
The signal in the signal is obtained after x times extraction. Therefore, the frequency band->
The distribution interval of the interference signal.
When x is in the interval [1, 2]]When the value is arbitrarily taken, the frequency band range of the interference signal is all frequency band intervals
Of (a), i.e
Where U represents the union of the sets. Therefore, in order to ensure that the baseband signal is not interfered by other signals after extraction, the extractor needs to filter out the frequency band
All signals within.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides the anti-interference extractor for extracting any multiple of 1-2 times and the design method thereof, and the extractor designed by the method has simple structure, is convenient to realize and can effectively inhibit interference.
In order to achieve the object of the invention, the following scheme is adopted:
the design method of the anti-interference extractor for extracting any multiple between 1 and 2 times is characterized in that the anti-interference extractor comprises the following steps: an anti-aliasing low pass filter and a polynomial interpolation filter;
the design method comprises the following steps:
s100, determining design parameters of an anti-aliasing low-pass filter and a polynomial interpolation filter, wherein the method comprises the following steps of:
determining the passband cut-off frequency of the anti-aliasing low-pass filter and the passband cut-off frequency of the polynomial interpolation filter according to the normalized bandwidth of the input signal;
selecting two frequency values in a preset frequency range, determining the stop band cut-off frequency of the anti-aliasing low-pass filter according to one frequency value, and determining the first stop band frequency range of the polynomial interpolation filter according to the other frequency value;
determining the number and the order of polynomials used by a polynomial interpolation filter;
s200, calculating coefficients of an anti-aliasing low-pass filter and a polynomial interpolation filter;
s300, respectively calculating the amplitude-frequency response of the anti-aliasing low-pass filter and the polynomial interpolation filter, and correspondingly multiplying the amplitude-frequency response of the anti-aliasing low-pass filter with the amplitude-frequency response of the polynomial interpolation filter according to frequency points to obtain the amplitude-frequency response of the anti-interference extractor;
s400, judging whether the interference suppression capability of the amplitude-frequency response of the anti-interference extractor in the interference frequency band reaches a preset interference suppression level threshold value:
if not, returning to the step S100, and re-executing the steps S100-S400;
if so, the anti-interference extractor is successfully designed.
Further, in step S100, the passband cut-off frequency of the anti-aliasing low pass filter
And passband cut-off frequency of polynomial interpolation filter +.>
Equal to the normalized bandwidth B of the input signal, i.e.>
Further, in step S100, in the frequency range
Two frequency values Deltaf are selected internally 1 And Δf 2 Let the stop band cut-off frequency of the anti-aliasing low pass filter be +.>
The first stop band frequency range of the polynomial interpolation filter is [ 1-delta f 2 ,1+Δf 2 ]。
Further, in step S400, the interference frequency band is:
an anti-interference extractor for extracting any multiple between 1 and 2 times, comprising:
the anti-aliasing low-pass filter is used for filtering out part of interference signals in an interference frequency band; and
The polynomial interpolation filter is connected with the anti-aliasing low-pass filter and is used for filtering the rest interference signals in the interference frequency band in cooperation with the anti-aliasing low-pass filter, and 1-2 times of extraction of the signals is realized in a resampling mode;
the anti-interference extractor is obtained by the design method of the anti-interference extractor for extracting any multiple of 1-2 times.
The embodiment of the invention has the beneficial effects that:
the anti-interference extractor for extracting 1-2 times any multiple obtained by the design method solves the problem that interference is caused by mixing an interference signal in a specific frequency band into the frequency band of a baseband signal after 1-2 times extraction in the prior art, effectively inhibits interference, and has simple structure and convenient implementation.
Drawings
The drawings described herein are for illustration of selected embodiments only and not all possible implementations, and are not intended to limit the scope of the invention.
Fig. 1 is a type I Farrow filter implementing a polynomial interpolation operation, where n=n 1 +N 2 +1 is the number of polynomials and M is the order of the polynomials.
Fig. 2 is a type II Farrow filter implementing a polynomial interpolation operation, where n=n 1 +N 2 +1 is the number of polynomials and M is the order of the polynomials.
FIG. 3 is a schematic diagram of adjacent channel interference phenomenon occurring when the polynomial interpolation filter performs 1-2 times of extraction.
Fig. 4 is a block diagram of an anti-interference extractor for 1-2 times any multiple extraction according to the present invention.
FIG. 5 is a magnitude-frequency response of an embodiment of an anti-interference decimator design of the present invention.
Detailed Description
To make the objects, technical solutions and advantages of the present invention more clear, an example of the design of an anti-interference extractor for extracting any multiple between 1-2 times is given for the method described in the present invention.
The structure diagram of the anti-interference extractor for extracting any multiple between 1-2 times provided by the invention is shown in fig. 4, and the anti-interference extractor comprises an anti-aliasing low-pass filter and a polynomial interpolation filter.
The design method of the anti-interference extractor for extracting any multiple between 1 and 2 times provided by the invention is as follows:
1. a normalized bandwidth B of the input signal is determined.
In this example, the normalized bandwidth of the input signal is taken to be 0.12, i.e., b=0.12.
2. A level of suppression of the interfering signal by the anti-interference decimator is determined.
In this example, the interference suppression level is taken to be 50dB.
3. The coefficients of the anti-aliasing low pass filter and the polynomial interpolation filter are jointly designed.
And 3.1, determining design parameters of the anti-aliasing low-pass filter and the polynomial interpolation filter.
a. Passband cut-off frequency of anti-aliasing low pass filter
And passband cut-off frequency of polynomial interpolation filter
Equal to the normalized bandwidth of the input signal, i.e.>
b. Two frequency values are selected within the frequency range [0.12,0.38): Δf 1 =0.175 and Δf 2 = 0.2425. Let the stop band cut-off frequency of the anti-aliasing low-pass filter be
The first stop band frequency range of the polynomial interpolation filter is [ 1-delta f 2 ,1+Δf 2 ]I.e. [0.7575 ] 2 ,1.2425]。
And c, determining the number N and the order M of polynomials used by the polynomial interpolation filter. In this example, n=4 and m=3 are taken.
And 3.2, calculating coefficients of the anti-aliasing low-pass filter and the polynomial interpolation filter based on a least square criterion or a best consistent approximation criterion. In this example, the coefficient of the anti-aliasing low pass filter calculated according to the least squares criterion is
There are two types of coefficients for a polynomial interpolation filter:
in this example, the coefficients for the type I Farrow filter calculated according to the least squares criterion are
Coefficients for a type II Farrow filter are
And 3.3, calculating the amplitude-frequency response of the anti-interference extractor.
First, the amplitude-frequency responses of the antialiasing low-pass filter and the polynomial interpolation filter are calculated, respectively.
Then, the amplitude-frequency responses of the anti-interference decimators are multiplied correspondingly according to the frequency points, so that the amplitude-frequency response of the anti-interference decimators is obtained.
In this example, the amplitude-frequency response of the immunity decimator is shown in FIG. 5.
3.4, judging that the amplitude-frequency response of the anti-interference extractor is in the interference frequency band
Whether the interference suppression capability in the system meets the design requirement.
Fig. 5 shows the amplitude-frequency response of the anti-interference decimator of this embodiment.
The solid line in the figure shows the amplitude-frequency response of the anti-interference decimator, and the dotted line shows the amplitude-frequency response of the polynomial interpolation filter.
It can be seen from the figure that the power gain of the anti-interference extractor in the interference frequency band [0.38,1.12] (the area between two black vertical lines in the figure) is < -50dB, i.e. the interference suppression capability reaches more than 50dB, thereby meeting the design requirement. Therefore, the interference signal can be effectively suppressed.
The polynomial interpolation filter has a power gain of > -8dB in the adjacent frequency band [0.38,0.5] of the input signal, and has poor effect of suppressing the interference signal.
The foregoing is merely a preferred embodiment of the present invention and is not meant to be the only or limiting of the present invention. It will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention.
Claims (3)
1. The design method of the anti-interference extractor for extracting any multiple between 1 and 2 times is characterized in that the anti-interference extractor comprises the following steps: an anti-aliasing low pass filter and a polynomial interpolation filter;
the design method comprises the following steps:
s100, determining design parameters of an anti-aliasing low-pass filter and a polynomial interpolation filter, wherein the method comprises the following steps of:
determining the passband cut-off frequency of an anti-aliasing low pass filter and the passband cut-off frequency of a polynomial interpolation filter based on the normalized bandwidth of the input signal
And passband cut-off frequency of polynomial interpolation filter +.>
Equal to the normalized bandwidth B of the input signal, i.e.>
In the frequency range
Two frequency values Deltaf are selected internally 1 And Δf 2 According to the frequency value Deltaf 1 Determining the stop band cut-off frequency of the anti-aliasing low-pass filter, so that the stop band cut-off frequency of the anti-aliasing low-pass filter is +.>
According to the frequency value Deltaf 2 Determining a first stop band frequency range of a polynomial interpolation filter, wherein the first stop band frequency range of the polynomial interpolation filter is [ 1-delta f ] 2 ,1+Δf 2 ]；
Determining the number and the order of polynomials used by a polynomial interpolation filter;
s200, calculating coefficients of an anti-aliasing low-pass filter and a polynomial interpolation filter;
s300, respectively calculating the amplitude-frequency response of the anti-aliasing low-pass filter and the polynomial interpolation filter, and correspondingly multiplying the amplitude-frequency response of the anti-aliasing low-pass filter with the amplitude-frequency response of the polynomial interpolation filter according to frequency points to obtain the amplitude-frequency response of the anti-interference extractor;
s400, judging whether the interference suppression capability of the amplitude-frequency response of the anti-interference extractor in the interference frequency band reaches a preset interference suppression level threshold value:
if not, returning to the step S100, and re-executing the steps S100-S400;
if so, the anti-interference extractor is successfully designed.
2. The method for designing an anti-interference decimator for 1-2 times any multiple of decimation according to claim 1, wherein in step S400, the interference frequency band is:
3. an anti-interference extractor for extracting any multiple between 1 and 2 times, comprising:
the anti-aliasing low-pass filter is used for filtering out part of interference signals in an interference frequency band; and
The polynomial interpolation filter is connected with the anti-aliasing low-pass filter and is used for filtering the rest interference signals in the interference frequency band in cooperation with the anti-aliasing low-pass filter, and 1-2 times of extraction of the signals is realized in a resampling mode;
the anti-interference extractor is obtained by the design method of the anti-interference extractor for extracting any multiple between 1 and 2 times according to the claim 1 or 2.
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