CN111327297A - Self-adaptive resampling method based on window function design - Google Patents

Self-adaptive resampling method based on window function design Download PDF

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CN111327297A
CN111327297A CN202010158691.3A CN202010158691A CN111327297A CN 111327297 A CN111327297 A CN 111327297A CN 202010158691 A CN202010158691 A CN 202010158691A CN 111327297 A CN111327297 A CN 111327297A
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resampling
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刘灏
林杰
毕天姝
熊文
王莉
危国恩
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North China Electric Power University
Guangzhou Power Supply Bureau of Guangdong Power Grid Co Ltd
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Guangzhou Power Supply Bureau of Guangdong Power Grid Co Ltd
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Abstract

The invention discloses a self-adaptive resampling method based on window function design, which comprises the steps of firstly establishing a universal resampling model based on a Farrow structure; establishing a fractional delay filter design model based on a window function method, and obtaining a multi-component fractional delay filter by using the model; constructing a fractional delay filter matrix on the basis of the obtained multi-component fractional delay filter; solving a Farrow structure sub-filter coefficient matrix C by using a least square method; and (4) substituting the obtained Farrow structure sub-filter coefficient matrix C into the resampling model established in the step (1) to complete the establishment of a universal Farrow structure resampling model. The method has better flexibility and smaller calculated amount, can obtain a proper model by adjusting the parameters for multiple times, simultaneously realizes sampling at any point, and has the function of arbitrary conversion between sampling rates.

Description

Self-adaptive resampling method based on window function design
Technical Field
The invention relates to the technical field of digital signal processing, in particular to a self-adaptive resampling method based on window function design.
Background
The resampling technology can realize conversion of any sampling rate and sampling of any point, and is widely used in the fields of signal processing, audio frequency, communication and the like, the key for realizing the resampling technology lies in designing a variable fractional delay digital filter for interpolation, and the current common methods for designing the variable fractional delay filter include a polyphase filter, a cascade integration comb filter (CIC) and a Farrow structure-based finite impulse response delay filter, and the like.
The key of the finite impulse response delay filter design based on the Farrow structure lies in the design of Farrow structure sub-filter coefficients, and the existing coefficient design methods include a Weighted Least square method (Weighted Least Squares), a minimum maximum method, an intelligent algorithm represented by a particle swarm algorithm and the like. The particle swarm optimization is only suitable for the condition that the coefficient dimension is low, and when the coefficient dimension is high, the algorithm cannot be further optimized; the minimum maximum method and the weighted least square method both aim at minimizing the design error, and the calculation amount of the design process is increased by the inversion operation of the process design matrix and the like, so that the defects of long design time and complex adjustment of weight parameters and the like exist.
Disclosure of Invention
The invention aims to provide a self-adaptive resampling method based on window function design, which has the advantages of good flexibility and small calculated amount, can obtain a proper resampling model by adjusting parameters, can realize sampling at any point by the obtained model, and has the function of arbitrary conversion between sampling rates.
The purpose of the invention is realized by the following technical scheme:
a method for adaptive resampling based on window function design, the method comprising:
step 1, firstly, establishing a universal resampling model based on a Farrow structure; wherein the established resampling model is represented as:
Figure BDA0002404981660000011
where k is the number of the resampled sequence, T2For the sampling period of resampling, yr(kT2) Is represented by T2A resampling sequence that is periodic; m is the number of the sample sequence, T1For the sampling period of the sampled signal, x (mT)1) Is represented by T1Is the sampling sequence of the sampling period, I is the order of the polynomial, I is the highest order, n is the number, c is the Farrow structure sub-filter coefficient, p ∈ [ -0.5,0.5]Represents a delay; [. the]Represents a rounding down operation;
step 2, establishing a fractional delay filter design model based on a window function method, and obtaining a multi-component delay filter coefficient by using the model;
step 3, constructing a coefficient matrix of the fractional delay filter on the basis of the obtained coefficients of the multi-component delay filter;
step 4, solving a Farrow structure sub-filter coefficient matrix C by using a least square method;
and 5, substituting the obtained Farrow structure sub-filter coefficient matrix C into the resampling model established in the step 1 to complete establishment of a universal Farrow structure resampling model.
The technical scheme provided by the invention can show that the method has good flexibility and small calculation amount, a proper resampling model can be obtained by adjusting the parameters, the obtained model can realize sampling at any point, and the method has the function of arbitrary conversion between sampling rates.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a self-adaptive resampling method based on window function design according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating comparison of amplitude-frequency characteristics of filters designed according to different window functions in an embodiment of the present invention;
FIG. 3 is a diagram illustrating a comparison of group delay characteristics for different window functions according to an exemplary embodiment of the present invention;
FIG. 4 is a schematic diagram showing the comparison of the amplitude-frequency characteristics of filters designed according to different parameters of a Kaiser window in the embodiment of the present invention;
FIG. 5 is a diagram illustrating a comparison of group delay characteristics designed by different parameters of a Kaiser window in an example of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The following will describe the embodiments of the present invention in further detail with reference to the accompanying drawings, and as shown in fig. 1, a schematic flow chart of an adaptive resampling method based on window function design provided by the embodiments of the present invention is shown, where the method includes:
step 1, firstly, establishing a universal resampling model based on a Farrow structure;
wherein the established resampling model is represented as:
Figure BDA0002404981660000031
where k is the number of the resampled sequence, T2For the sampling period of resampling, yr(kT2) Is represented by T2A resampling sequence that is periodic; m is the number of the sample sequence, T1For the sampling period of the sampled signal, x (mT)1) Is represented by T1Is the sampling sequence of the sampling period, I is the order of the polynomial, I is the highest order, n is the number, c is the Farrow structure sub-filter coefficient, p ∈ [ -0.5,0.5]Represents a delay; [. the]Indicating a rounding down operation.
The process of establishing the model specifically comprises the following steps:
first, the signal reconstruction model in the ideal case is represented as:
Figure BDA0002404981660000032
wherein x (t) is the original signal; h (t) is the impulse response of the ideal low-pass filter; y isr(t) is the reconstructed signal;
for the reconstructed signal yr(t) resampling to obtain resample values expressed as:
Figure BDA0002404981660000033
to ensure that no frequency aliasing occurs during resampling, the sampling period T is chosen for different resampling cycles2The required cut-off frequency of the low-pass filter is different, the order of the corresponding filter is also different, and the order of the filter required for realizing resampling can follow the sampling period T2The Farrow structure model is thus applied in the resampling model, specifically:
the impulse response h (t) of the ideal low-pass filter is expressed by a constant-length piecewise polynomial function:
Figure BDA0002404981660000034
in the formula, N represents the number of polynomials; Δ is the segment length; n is the number of a polynomial, anThe polynomial is an nth section polynomial, and the specific expression is as follows:
Figure BDA0002404981660000035
c represents Farrow structure sub-filter coefficients, which are also polynomial coefficients; the variable range in the t/delta-0.5 control polynomial is [ -0.5,0.5 [)]A is mixing the above-mentionednSubstituting the expression into the impulse response h (t) of the ideal low-pass filter to obtain:
Figure BDA0002404981660000036
substituting the above-mentioned expression h (T) into the signal reconstruction model in order to make h (T) follow the resampling sampling period T2Transform, with de-aliasing properties, by taking Δ ═ T2And obtaining a resampling model based on a Farrow structure as follows:
Figure BDA0002404981660000041
the key of the above resampling model based on Farrow structure is the design of the Farrow structure sub-filter coefficient c, which will determine the effect of the filter.
As can be seen from the resampling model, the resample value yr(kT2) Can be regarded as a sampled value x (mT)1) Convolving with the unit impulse response h (n) of the digital filter, wherein the unit impulse response h (n) can be expressed by a polynomial form.
Step 2, establishing a fractional delay filter design model based on a window function method, and obtaining a multi-component delay filter coefficient by using the model;
in this step, because the frequency domain characteristic of the ideal low-pass filter is limited bandwidth, the time domain impulse response of the ideal low-pass filter needs to be infinite length, and the filter in practice cannot meet the requirement of infinite length, the practical realization needs to consider the impulse response to be cut off, the window function can achieve a good cut-off effect, and the establishment process of the fractional delay filter design model based on the window function method is as follows:
first, the linear phase FIR low-pass digital filter can be obtained by truncating an ideal low-pass filter by using a window function, and then the unit impulse response h (n) of the FIR digital filter is expressed as:
h(n)＝hd(n)·w(n)0≤n≤N-1；
in the formula, N-1 is the order of the filter coefficient; h isd(n) is the unit impulse response of the ideal low-pass digital filter; w (N) is a window function of length N; the FIR digital filter designed by this model has no delay.
hdThe expression of (n) is:
Figure BDA0002404981660000042
in the formula, ωcIs the filter cut-off frequency; τ is the group delay of the filter;
because the selection of the window function has decisive significance on the filter characteristics, different window functions and corresponding parameters thereof can determine the leakage coefficient, sidelobe attenuation and main lobe width of the window function, and further can influence the passband range, transition band length and stop band of the filter, the Keze window pair h with stronger adaptability is selected in the applicationd(n) performing truncation, wherein the Kaiser window model is as follows:
Figure BDA0002404981660000043
wherein β is an optional parameter and can effectively regulate the width of the main lobe and the attenuation of the side lobe I0(. is) a first class of zeroth order variant Bessel functions modeled as:
Figure BDA0002404981660000051
mixing the above hdSubstituting the models of (n) and w (n) into the model of h (n), wherein the obtained group delay characteristic of the filter is tau;
to obtain a fractional delay filter, the sequence n is further shifted, and the model is expressed as:
h(n-p)＝hd(n-p)·w(n-p) 0≤n≤N-1
in the formula, p is the delay in step 1, and the group delay of the designed fractional delay filter is τ + p. In the delay range of-0.5, a plurality of numbers are taken as delay amount p in sequence, and multi-component delay filter coefficients can be designed.
In specific implementation, the frequency characteristics of the filter can be further adjusted by modifying the adopted window function parameters and the cut-off frequency of the filter, and the filter capable of meeting the requirements is designed.
Step 3, constructing a coefficient matrix of the fractional delay filter on the basis of the obtained coefficients of the multi-component delay filter;
in this step, on the basis of the obtained multi-component delay filter coefficients, a fractional delay filter coefficient matrix is constructed, the matrix being represented by the form:
Figure BDA0002404981660000052
in the formula, hpkRepresenting a delay of pkFilter coefficient of hpk＝[hpk(0),hpk(1),……,hpk(N-1)]。
Step 4, solving a Farrow structure sub-filter coefficient matrix C by using a least square method;
in this step, the process of solving the Farrow structure sub-filter coefficient matrix C by using the least square method specifically includes:
the unit impulse response h (n) of the filter expressed by the piecewise polynomial is:
Figure BDA0002404981660000053
expressing the constructed coefficient matrix of the fractional delay filter by a polynomial structure, and obtaining an expression of a matrix form as follows:
Figure BDA0002404981660000054
in which the first term on the right is the delay pkAnd the corresponding power, which can be represented by a matrix P, the second term is a Farrow structure sub-filter coefficient matrix, which is represented by a matrix C, and the left term filter coefficient matrix is represented by H. The above expression is then simplified to:
H＝P·C；
solving a matrix C in the expression by a least square method to obtain a C expression as follows:
C＝(PTP)-1PTH
and 5, substituting the obtained Farrow structure sub-filter coefficient matrix C into the resampling model established in the step 1 to complete establishment of a universal Farrow structure resampling model.
The built universal Farrow structure resampling model can realize sampling at any point, and has the function of randomly converting sampling rates.
In order to more clearly show the technical solutions and the technical effects provided by the present invention, the following describes in detail a simulation test example of the adaptive resampling method based on window function design provided by the present invention, which specifically includes:
1. influence of the kind of window function used on the filter characteristics
To reflect the influence of the type of window function on the characteristics of the filter during the design of the fractional delay filter, the filter design is performed by taking a hanning window, a blackman window and a keze window as examples, and the design results are shown in table 1 below, wherein the simulation shows that the filter order is 39, the offset p is 0.1, and the parameter β of the keze window is 12 in table 1εaThe expression is epsilon for the range of amplitude error in the passband rangea＝20log(|H(ω,p)-Hd(ω,p)|,ω∈[0,0.8π],p∈[-0.5,0.5])，ε∞For the maximum amplitude error in the passband, the expression is ε∞＝20log(max{|H(ω,p)-Hd(ω,p)|,ω∈[0,0.8π],p∈[-0.5,0.5]})，εgFor the maximum group delay error in the passband, the expression is εg＝max{|τ(ω,p)-p|,ω∈[0,0.8π],p∈[-0.5,0.5]}。
TABLE 1 Effect of Window function type on Filter characteristics
Figure BDA0002404981660000061
The results show that not all window functions can be applied to the design of the fractional delay filter. Epsilon∞Can reflect the anti-noise capability of the filter, epsilongWhether the group delay of the filter has larger deviation can be reflected, as shown in fig. 2, a comparison schematic diagram of amplitude-frequency characteristics of the filter designed by different window functions in the embodiment of the invention is shown, as shown in fig. 3, a comparison schematic diagram of group delay characteristics designed by different window functions is shown, and as can be seen from comparison of design results of a hanning window, a blackman window and a kezeer window, the kezer window with strong adaptability has the best design effect.
2. The influence of the parameters of the Keiser window used on the characteristics of the filter
The high adaptability of the keze window is reflected in the adjustment of the parameter β, and therefore, the significance of the window function parameter in designing the fractional delay filter is reflected by aiming at a plurality of parameters β, and the design result is shown in the following table 2:
TABLE 2 Effect of Window function parameters on Filter characteristics
Figure BDA0002404981660000071
When β is smaller, the window function has leakage coefficient to cause the stability of the filter to be worse, and with the increase of β, the side lobe attenuation of the window function increases to reduce the pass band range, so that the proper parameter β can be selected for different requirements, as shown in fig. 4, a schematic diagram of amplitude-frequency characteristics of the filter designed by different parameters of a kaiser window in the example of the invention, and as shown in fig. 5, a schematic diagram of group delay characteristics designed by different parameters of the kaiser window.
3. The method is compared with the design result of a classic WLS algorithm
The algorithm contrast control simulation parameters are consistent as follows: the order of the filter is 39, and the passband is in the range of 0,0.8 pi]Delay p ∈ [ -0.5,0.5 [ ]]The polynomial order is 8. In order to achieve the desired effect, the filter cut-off frequency ω is taken in this examplecAnd (3) selecting a Keyzing window by the window function, and taking 12 as the Keyzing window parameter Beta.
Under the requirement of simulation parameters, the solving result of the method is compared with the fractional delay filter characteristic corresponding to the solving result of the WLS algorithm, and the comparison result is shown in the following table 3:
TABLE 3 comparison of algorithms
Figure BDA0002404981660000072
The result shows that the filter characteristic designed by the method can achieve the effect similar to the filter characteristic optimally designed by the traditional method, and the method has a better design result than the weighted least square method in the aspect of group delay.
Due to filter cut-off frequency omegacThe gain at the corresponding position is 0.5, so when ω iscFilters designed at pi do not suppress signals at more than half the resampling frequency effectively. In order to prevent the occurrence of frequency aliasing, it is required to control the stopband cutoff frequency of the filter to be pi. For this purpose, two algorithms are used to redesign the Farrow sub-filter coefficients, and the comparison result is shown in table 4 below, in the simulation parameters, the filter order is 39, and the passband is in the range of [0,0.5 π ]]Delay p ∈ [ -0.5,0.5 [ ]]Polynomial order of 8 order, filter cut-off frequency omegacThe 0.76 pi kelze window parameter Beta takes 16.
TABLE 4 comparison of algorithms
Figure BDA0002404981660000081
The result shows that the filter can be flexibly designed according to the requirement of the pass band range, but the weighted least square method can not realize the design, and the reason for the method is that when the pass band range is small, the optimal solution error corresponding to the optimal design method is large, a singular matrix can appear in the operation process, and the calculation can not be directly carried out. In contrast, the method of the present application does not need to involve these calculations, and the passband of the fractional delay filter is controlled directly by the window function, thereby satisfying the design requirements.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
In summary, the method provided by the present application can flexibly modify the order, the cut-off frequency and the window function parameter of the filter, so that the frequency characteristic of the filter can meet the actual requirement; compared with the traditional design method, the method has better flexibility and small calculated amount, and can obtain a proper model by adjusting the parameters for many times.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. An adaptive resampling method based on window function design, characterized in that the method comprises:
step 1, firstly, establishing a universal resampling model based on a Farrow structure; wherein the established resampling model is represented as:
Figure FDA0002404981650000011
where k is the number of the resampled sequence, T2For the sampling period of resampling, yr(kT2) Is represented by T2A resampling sequence that is periodic; m is the number of the sample sequence, T1For the sampling period of the sampled signal, x (mT)1) Is represented by T1Is the sampling sequence of the sampling period, I is the order of the polynomial, I is the highest order, n is the number, c is the Farrow structure sub-filter coefficient, p ∈ [ -0.5,0.5]Represents a delay; [. the]Represents a rounding down operation;
step 2, establishing a fractional delay filter design model based on a window function method, and obtaining a multi-component delay filter coefficient by using the model;
step 3, constructing a coefficient matrix of the fractional delay filter on the basis of the obtained coefficients of the multi-component delay filter;
step 4, solving a Farrow structure sub-filter coefficient matrix C by using a least square method;
and 5, substituting the obtained Farrow structure sub-filter coefficient matrix C into the resampling model established in the step 1 to complete establishment of a universal Farrow structure resampling model.
2. The adaptive resampling method designed based on the window function as claimed in claim 1, wherein in step 1, the general resampling model building process based on Farrow structure is specifically:
first, the signal reconstruction model in the ideal case is represented as:
Figure FDA0002404981650000012
wherein x (t) is the original signal; h (t) is the impulse response of the ideal low-pass filter; y isr(t) is the reconstructed signal;
for the reconstructed signal yr(t) resampling to obtain resample values expressed as:
Figure FDA0002404981650000013
for different resampling sample periods T2The required cut-off frequency of the low-pass filter is different, the order of the corresponding filter is also different, and the order of the filter required for realizing resampling can follow the sampling period T2The Farrow structure model is thus applied in the resampling model, specifically:
the impulse response h (t) of the ideal low-pass filter is expressed by a constant-length piecewise polynomial function:
Figure FDA0002404981650000021
in the formula, N represents the number of polynomials; Δ is the segment length; a isnThe method is an nth section polynomial expression and specifically expressed as follows:
Figure FDA0002404981650000022
c represents Farrow structure sub-filter coefficients, which are also polynomial coefficients; the variable range in the t/delta control polynomial is [ -0.5,0.5 [)]A is mixing the above-mentionednSubstituting the expression into the impulse response h (t) of the ideal low-pass filter to obtain:
Figure FDA0002404981650000023
substituting the above-mentioned expression h (T) into the signal reconstruction model in order to make h (T) follow the resampling sampling period T2Transform, with de-aliasing properties, by taking Δ ═ T2And obtaining a resampling model based on a Farrow structure as follows:
Figure FDA0002404981650000024
the key of the above resampling model based on Farrow structure is the design of the Farrow structure sub-filter coefficient c, which will determine the effect of the filter.
3. The adaptive resampling method designed based on window function as claimed in claim 1, wherein in step 2, the fractional delay filter design model based on window function method is built by:
first, the linear phase FIR low-pass digital filter can be obtained by truncating an ideal low-pass filter by using a window function, and then the unit impulse response h (n) of the FIR digital filter is expressed as:
h(n)＝hd(n)·w(n)0≤n≤N-1；
in the formula, N-1 is the order of the filter coefficient; h isd(n) is the unit impulse response of the ideal low-pass digital filter; w (N) is a window function of length N; the FIR digital filter designed by the model has no delay;
hdthe expression of (n) is:
Figure FDA0002404981650000025
in the formula, ωcIs the filter cut-off frequency; τ is the group delay of the filter;
then select Kaiser window pair hd(n) performing truncation, wherein the Kaiser window model is as follows:
Figure FDA0002404981650000026
wherein β is an optional parameter and can effectively regulate the width of the main lobe and the attenuation of the side lobe I0(. is) a first class of zeroth order variant Bessel functions modeled as:
Figure FDA0002404981650000031
mixing the above hdSubstituting the models of (n) and w (n) into the model of h (n), wherein the obtained group delay characteristic of the filter is tau;
to obtain the fractional delay filter coefficients, the sequence n is further shifted, and the model is expressed as:
h(n-p)＝hd(n-p)·w(n-p)0≤n≤N-1
the group delay of the coefficient of the designed fractional delay filter is corresponding to tau + p; and taking a plurality of delay quantities p and designing coefficients of the multi-component delay filter.
4. The adaptive resampling method designed based on the window function as claimed in claim 1, wherein in step 2, the frequency characteristic of the filter is adjusted by further modifying the parameters of the window function and the cut-off frequency of the filter, so as to design a filter that can meet the requirement.
5. The adaptive resampling method designed based on the window function as claimed in claim 1, wherein in step 3, the process of constructing the fractional delay filter coefficient matrix is specifically:
on the basis of the obtained multi-component delay filter coefficients, constructing a coefficient matrix of the fractional delay filter as follows:
Figure FDA0002404981650000034
in the formula, hpkRepresenting a delay of pkFilter coefficient of hpk＝[hpk(0),hpk(1),……,hpk(N-1)]。
6. The adaptive resampling method designed based on the window function as claimed in claim 1, wherein in step 4, the process of solving the Farrow structure sub-filter coefficient matrix C by using the least square method specifically comprises: :
the unit impulse response h (n) of the filter expressed by the piecewise polynomial is:
Figure FDA0002404981650000032
expressing the constructed coefficient matrix of the fractional delay filter by a polynomial structure, and obtaining an expression of a matrix form as follows:
Figure FDA0002404981650000033
in which the first term on the right is the delay pkAnd the corresponding power, which can be represented by a matrix P; the second term is a Farrow structure sub-filter coefficient matrix which is represented by a matrix C; the left term filter coefficient matrix is denoted by H;
the above expression is then simplified to:
H＝P·C；
solving a matrix C in the expression by a least square method to obtain a C expression as follows: c ═ PTP)-1PTH。
CN202010158691.3A 2020-03-09 2020-03-09 Self-adaptive resampling method based on window function design Pending CN111327297A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112865749A (en) * 2021-01-18 2021-05-28 中国船舶重工集团公司第七二四研究所 Design method of variable fractional delay filter with symmetric coefficients
CN114221637A (en) * 2021-11-25 2022-03-22 北京理工大学 Segmented decimal time-delay filtering method based on coefficient relation structure

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107342750A (en) * 2017-07-04 2017-11-10 电子科技大学 Fractional delay optimization method suitable for more Nyquist areas and its realize structure
CN108322299A (en) * 2018-01-10 2018-07-24 北京哨兵科技有限公司 A kind of inclined analog signal generating method of code and device
CN109088617A (en) * 2018-09-20 2018-12-25 电子科技大学 Ratio variable number resampling filter
CN110708039A (en) * 2019-09-17 2020-01-17 广西师范大学 Coefficient fitting method of FARROW filter

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107342750A (en) * 2017-07-04 2017-11-10 电子科技大学 Fractional delay optimization method suitable for more Nyquist areas and its realize structure
CN108322299A (en) * 2018-01-10 2018-07-24 北京哨兵科技有限公司 A kind of inclined analog signal generating method of code and device
CN109088617A (en) * 2018-09-20 2018-12-25 电子科技大学 Ratio variable number resampling filter
CN110708039A (en) * 2019-09-17 2020-01-17 广西师范大学 Coefficient fitting method of FARROW filter

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
张盛耀: "软件无线电中用于采样速率转换的Farrow结构滤波器设计" *
王亚萍 等: "基于数字滤波的光纤光栅传感信号去噪及其FPGA实现" *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112865749A (en) * 2021-01-18 2021-05-28 中国船舶重工集团公司第七二四研究所 Design method of variable fractional delay filter with symmetric coefficients
CN114221637A (en) * 2021-11-25 2022-03-22 北京理工大学 Segmented decimal time-delay filtering method based on coefficient relation structure
CN114221637B (en) * 2021-11-25 2024-06-11 北京理工大学 Segmented decimal time delay filtering method based on coefficient relation structure

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