Interpolation fir filter optimization method and device, electronic equipment
By generating interpolation FIR filters with symmetric structures through splitting, zero-insertion, and polyphase decomposition, the problems of excessive multiplication operations and loss of coefficient symmetry are solved, achieving efficient filter optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHENGDU WEIDE QINGYUN ELECTRONICS CO LTD
- Filing Date
- 2026-05-27
- Publication Date
- 2026-08-04
AI Technical Summary
Existing technologies in direct-type FIR filters involve numerous multiplication operations, and the loss of coefficient symmetry after polyphase decomposition causes the filter to malfunction, lacking effective methods for phase information recovery.
The interpolation FIR filter is split into multiple phase sub-filters. Through zero-plugging and polyphase decomposition, a coefficient combination with a symmetric structure is generated. Symmetric folding and restoration are then performed to ensure the correctness of the filtering results.
It effectively reduces the number of interpolation filter multiplication operations by half, adapts to arbitrary interpolation ratios and coefficient lengths, and ensures the correctness of the filtering results.
Smart Images
Figure CN122316284B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing technology, and in particular to an interpolation FIR filter optimization method and apparatus, and electronic equipment. Background Technology
[0002] With the rapid development of modern wireless communication technology, multi-rate signal processing is frequently required. FIR filters are often used as the core unit for rate signal processing, and interpolation FIR is an efficient means of improving signal sampling rate. When implementing interpolation FIR with a traditional direct-form structure, the number of multiplication operations is the same as the filter length N. In FPGAs, each multiplication operation requires a DSP hard core. To obtain sufficient stopband attenuation and passband flatness, the filter order is significantly increased. Therefore, reducing the number of multiplication operations becomes crucial for improving the performance of interpolation FIR.
[0003] Traditional linear-phase FIR filter coefficients possess symmetry. Utilizing this property, the number of multiplications can be reduced from K to K / 2, a method widely adopted in direct-type FIR structures. Furthermore, polyphase structures can avoid redundant zero-multiplication operations in interpolation filtering, reducing the number of multiplications to K / L (where L is the interpolation factor), thus improving filtering speed. However, when the filter coefficient length is not an integer multiple of the interpolation factor, polyphase decomposition causes the filter to lose symmetry, making "symmetrical folding" impossible in polyphase structures. Moreover, while existing techniques address the loss of symmetry after polyphase decomposition for specific coefficient lengths, they modify the original coefficients, altering the phase information, without providing a method to restore the coefficient phase and obtain the correct filtering result. Summary of the Invention
[0004] The purpose of this invention is to provide an interpolation FIR filter optimization method, apparatus, and electronic device, so as to at least solve the problem of how to reduce the number of FIR filter multiplication operations by using a polyphase structure with coefficients of arbitrary length.
[0005] To address the aforementioned technical problems, this invention provides an interpolation FIR filter optimization method, comprising: Based on the interpolation factor, the interpolation FIR filter is split into multiple phase sub-filters; Based on the relationship between the original coefficient length and the interpolation ratio of the interpolated FIR filter, the original coefficient length is zero-placing to obtain the target coefficient length. The target coefficient length is decomposed into multiple phases to obtain a new coefficient structure; Add or subtract the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure. Symmetrical folding is performed on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; The output signal of the phase sub-filter is recovered to obtain the filtering result of the interpolation FIR filter.
[0006] Optionally, in the interpolation FIR filter optimization method, the method of splitting the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio includes: Based on the interpolation factor L, the interpolation FIR filter is divided into L phase sub-filters.
[0007] Optionally, in the interpolation FIR filter optimization method, all the phase sub-filters have the same length.
[0008] Optionally, in the interpolation FIR filter optimization method, the method of performing zero-placing on the original coefficient length based on the relationship between the original coefficient length and the interpolation ratio of the interpolation FIR filter to obtain the target coefficient length includes: If the original coefficient length cannot be divided evenly by the interpolation factor, then zero-placing is performed on the original coefficient length to obtain the target coefficient length; Otherwise, the original coefficient length is used directly as the target coefficient length.
[0009] Optionally, in the interpolation FIR filter optimization method, the method of inserting zeros into the original coefficient length to obtain the target coefficient length if the original coefficient length cannot be divided by the interpolation factor includes: If the interpolation factor is even and the original coefficient length is odd-symmetric, then an odd number of zero values are inserted into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor. Otherwise, insert an even number of zero values into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor.
[0010] Optionally, in the interpolation FIR filter optimization method, the number of odd-numbered zero values inserted into the original coefficient length is:
[0011] Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. Indicates rounding up; The number of zero values inserted at the beginning of the original coefficient length is M / 2, and the number of zero values inserted at the end of the original coefficient length is (M+1) / 2.
[0012] Optionally, in the interpolation FIR filter optimization method, the number of even-number zero values inserted into the original coefficient length is:
[0013] Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. Indicates rounding down; The number of zero values inserted at the beginning and end of the original coefficient length is M / 2, respectively.
[0014] Optionally, in the interpolation FIR filter optimization method, the method of adding or subtracting the polyphase coefficients of the new coefficient structures of the corresponding two phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure includes: The i-th phase sub-filter and the L-1-i-th phase sub-filter are regarded as two corresponding phase sub-filters, where L represents the number of phase sub-filters; The polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are added together, and the result is used as the target polyphase coefficient of the i-th phase sub-filter. The polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are subtracted, and the result is used as the target polyphase coefficient of the L-1-i-th phase sub-filter. Integrate the target polyphase coefficients of all phase sub-filters to obtain a coefficient symmetric combination with a symmetric structure.
[0015] Optionally, in the interpolation FIR filter optimization method, the method of adding or subtracting the polyphase coefficients of the new coefficient structures of the corresponding two phase sub-filters to obtain the target polyphase coefficient length of the symmetrical structure further includes: When the number of phase sub-filters is odd, the polyphase coefficients of the new coefficient structure of the (L-1) / 2th phase sub-filter are the target polyphase coefficients of the (L-1) / 2th phase sub-filter.
[0016] Optionally, in the interpolation FIR filter optimization method, the method of performing symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter includes: The i-th phase sub-filter is operated in pre-addition mode, and the operation process is expressed as follows:
[0017] The L-1-i-th phase sub-filter is operated in pre-decrease mode, and the operation process is expressed as follows:
[0018] Where N represents the original coefficient length and L represents the interpolation factor. This represents the target polyphase coefficient of the i-th phase sub-filter. Indicates the input signal. Let represent the output signal of the i-th phase sub-filter at time n, and k represent the sub-filter coefficient index.
[0019] Optionally, in the interpolation FIR filter optimization method, the method for recovering the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter includes: The output signal of the i-th phase sub-filter is subtracted from the output signal of the L-1-i-th phase sub-filter and then multiplied by 1 / 2. The result is used as the filtering result of the i-th phase of the interpolation FIR filter. The output signal of the i-th phase sub-filter is added to the output signal of the L-1-i-th phase sub-filter and then multiplied by 1 / 2. The result is used as the filtering result of the L-1-i-th phase of the interpolation FIR filter. The filtering results of the i-th phase of the interpolated FIR filter and the filtering results of the L-1-i-th phase of the interpolated FIR filter are integrated to obtain the filtering result of the interpolated FIR filter.
[0020] To address the aforementioned technical problems, the present invention also provides an interpolation FIR filter optimization device for implementing the interpolation FIR filter optimization method as described in any of the preceding claims, wherein the interpolation FIR filter optimization device comprises: The splitting module is used to split the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio; The zero-insertion module is used to perform zero-insertion processing on the original coefficient length based on the relationship between the original coefficient length and the interpolation ratio of the interpolated FIR filter, so as to obtain the target coefficient length. The decomposition module is used to perform multiphase decomposition on the target coefficient length to obtain a new coefficient structure; The arithmetic module is used to perform addition and subtraction operations on the polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure. The folding module is used to perform symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; The recovery module is used to recover the output signal of the phase sub-filter to obtain the filtering result of the interpolated FIR filter.
[0021] To address the aforementioned technical problems, the present invention also provides an electronic device, including a memory, a processor, and an executable program stored in the memory and executable by the processor; when the processor runs the executable program, it performs the interpolation FIR filter optimization method as described in any of the preceding claims.
[0022] The present invention provides an interpolation FIR filter optimization method, apparatus, and electronic device, comprising: decomposing the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio; performing zero-placing on the original coefficient length according to the relationship between the original coefficient length of the interpolation FIR filter and the interpolation ratio to obtain a target coefficient length; performing polyphase decomposition on the target coefficient length to obtain a new coefficient structure; performing addition and subtraction operations on the polyphase coefficients of the new coefficient structures of two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure; performing symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; and performing recovery processing on the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter. By performing zero-placing on the coefficient length to meet the coefficient symmetry requirements after polyphase decomposition, not only can the number of interpolation filtering multiplication operations be effectively reduced by half, but it can also adapt to arbitrary interpolation ratios and coefficient lengths; by performing recovery processing after obtaining the output signal of each phase sub-filter, the coefficient phase information can be efficiently restored, ensuring the correctness of the filtering result, thus solving the problem of how to reduce the number of FIR filter multiplication operations using a polyphase structure with coefficients of arbitrary length. Attached Figure Description
[0023] Figure 1 This is a flowchart of the interpolation FIR filter optimization method provided in this embodiment; Figure 2 This is a schematic diagram of the polyphase filter structure provided in this embodiment; Figure 3 This is a schematic diagram of the interpolation FIR filter optimization device provided in this embodiment. Detailed Implementation
[0024] The interpolation FIR filter optimization method, apparatus, and electronic device proposed in this invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the drawings are all in a very simplified form and use non-precise scales, used only to facilitate and clarify the illustration of the embodiments of this invention. Furthermore, the structures shown in the drawings are often part of the actual structure. In particular, different figures may emphasize different aspects and sometimes use different scales.
[0025] It should be noted that the terms "first," "second," etc., used in the specification, claims, and drawings of this invention are used to distinguish similar objects in order to describe embodiments of the invention, and are not used to describe a specific order or sequence. It should be understood that such uses of terminology are interchangeable where appropriate. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0026] To clearly explain the implementation scheme of the interpolation FIR filter optimization method, apparatus, and electronic device provided in this embodiment, the technical terms involved in this embodiment are explained as follows: FIR: Finite Impulse Response; DSP: Digital Signal Processor; FPGA: Field-Programmable Gate Array; Transfer function: The ratio of the output to the Laplace transform of the input for a linear time-invariant system under the initial condition of zero external input; Difference equations: Algebraic equations that describe the linear weighted relationship between the output sequence and the input sequence in a discrete-time system; Multiphase decomposition: The finite impulse response h[n] is divided into L subsequences (phases) according to the interpolation (or decimation) factor L, resulting in L FIR sub-filters (multiphase components) with shorter coefficients. This transforms high-order filtering operations into parallel, low-order, low-sampling-rate operation structures, which are used to efficiently realize decimation, interpolation, subband coding and multi-level rate conversion.
[0027] For an FIR filter with coefficient length (number of taps) of N and order N-1, its transfer function is expressed as:
[0028] And its difference equation is expressed as:
[0029] Assuming the interpolation factor is L, then the input signal The filtered signal output after interpolation filtering The time-domain relationship is expressed as:
[0030] For the aforementioned FIR filter, this embodiment provides an interpolation FIR filter optimization method, such as... Figure 1 As shown, it includes: S1, based on the interpolation factor, the interpolation FIR filter is split into multiple phase sub-filters; S2, based on the relationship between the original coefficient length and the interpolation factor of the interpolated FIR filter, the original coefficient length is zero-placing to obtain the target coefficient length; S3, perform multiphase decomposition on the target coefficient length to obtain a new coefficient structure; S4, perform addition and subtraction operations on the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure; S5, symmetrical folding is performed on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; S6 performs recovery processing on the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter.
[0031] The interpolation FIR filter optimization method provided in this embodiment satisfies the coefficient symmetry requirement after polyphase decomposition by inserting zeros into the coefficient length. This not only effectively reduces the number of interpolation filter multiplication operations by half, but also adapts to arbitrary interpolation ratios and coefficient lengths. By performing recovery processing after obtaining the output signal of each phase sub-filter, the coefficient phase information can be efficiently restored, ensuring the correctness of the filtering result. This solves the problem of how to reduce the number of FIR filter multiplication operations using a polyphase structure with coefficients of arbitrary length.
[0032] Specifically, in this embodiment, step S1 involves splitting the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio.
[0033] In practical applications, the interpolation FIR filter can be divided into L phase sub-filters according to the interpolation ratio L. Furthermore, to maintain the symmetry of each phase sub-filter, in this embodiment, all the phase sub-filters have the same length (coefficient length).
[0034] Furthermore, in this embodiment, in step S2, the original coefficient length is zero-placing is performed on the original coefficient length according to the relationship between the original coefficient length and the interpolation ratio of the interpolation FIR filter to obtain the target coefficient length.
[0035] Specifically, in this embodiment, different zero-placing processes are performed depending on whether the original coefficient length can be divided by the interpolation factor. If the original coefficient length cannot be divided by the interpolation factor, zero-placing is performed on the original coefficient length to obtain the target coefficient length; otherwise, the original coefficient length is directly used as the target coefficient length.
[0036] In practical applications, zero-placing of the original coefficient length is handled in the following two ways: Scenario 1: The interpolation factor is even, and the original coefficient length is odd-symmetric. In this case, an odd number of zero values are inserted into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor.
[0037] Specifically, in this embodiment, the number of odd-numbered zero values inserted into the original coefficient length is:
[0038] Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. This indicates rounding up to the nearest integer.
[0039] For example, in one example, the interpolation factor L is 4, the original coefficient length N is 15, and the original coefficient length is represented as h(n)={a,b,c,d,e,f,g,h,g,f,e,d,c,b,a}. Using the above formula, we can calculate M as 5, which means that 5 zero values need to be inserted into the original coefficient length.
[0040] Furthermore, in order to ensure that the target coefficient length obtained after zero insertion is symmetrical, in this embodiment, the number of zero values inserted at the beginning of the original coefficient length is M / 2, and the number of zero values inserted at the end of the original coefficient length is (M+1) / 2.
[0041] Taking the example above, inserting two zeros at the beginning and three zeros at the end of the original coefficient length, the resulting target coefficient length can be expressed as h(n)={0,0,a,b,c,d,e,f,g,h,g,f,e,d,c,b,a,0,0,0}.
[0042] Case 2: All cases other than Case 1. In this case, an even number of zero values are inserted into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor.
[0043] Specifically, in this embodiment, the number of even-number zero values inserted into the original coefficient length is:
[0044] Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. This indicates rounding down to the nearest integer.
[0045] For example, in one example, the interpolation factor L is 4, the original coefficient length N is 14, and the original coefficient length is represented as h(n)={a,b,c,d,e,f,g,g,f,e,d,c,b,a}. Using the above formula, we can calculate M as 2, which means that 2 zero values need to be inserted into the original coefficient length.
[0046] Furthermore, in order to ensure that the target coefficient length obtained after zero insertion is symmetrical, in this embodiment, the number of zero values inserted at the beginning and end of the original coefficient length is M / 2, respectively.
[0047] Taking the example above, inserting a 0 at the beginning and a 0 at the end of the original coefficient length, the resulting target coefficient length can be expressed as h(n)={0,a,b,c,d,e,f,g,g,f,e,d,c,b,a,0}.
[0048] Thus, by padding the original coefficient length with zeros to compensate for the filter length, the target coefficient length obtained meets the requirements of polyphase decomposition, ensuring that the coefficient lengths of each subsequent phase sub-filter are consistent.
[0049] Furthermore, in this embodiment, step S3 involves performing multiphase decomposition on the target coefficient length to obtain a new coefficient structure.
[0050] The specific implementation of multiphase decomposition of the target coefficient length is something that those skilled in the art can obtain based on the prior art, and this application will not elaborate on it further.
[0051] Taking the example used in the above scenario one, the target coefficient length h(n)={0,0,a,b,c,d,e,f,g,h,g,f,e,d,c,b,a,0,0,0} after multiphase decomposition, the multiphase coefficient lengths of the new coefficient structure obtained include: r0={0,d,g,b}, r1={0,e,f,a}, r2={a,f,e,0}, r3={b,g,d,0}, r4={c,h,c,0}. It can be seen that r0 and r3 are a pair of symmetries, r1 and r2 are a pair of symmetries, and r4 already has symmetry.
[0052] Taking the strength used in scenario two above as an example, the target coefficient length h(n) = {0,a,b,c,d,e,f,g,g,f,e,d,c,b,a,0}, after multiphase decomposition, the multiphase coefficient lengths of the new coefficient structure obtained include: r0 = {0,d,g,c}, r1 = {a,e,f,b}, r2 = {b,f,e,a}, r3 = {c,g,d,0}. It can be seen that r0 and r3 are a pair of symmetric pairs, and r1 and r2 are a pair of symmetric pairs.
[0053] For ease of explanation of subsequent steps, in this embodiment, the target coefficient length is represented as h(n)={h(0),h(1),h(2),…,h(N'-1)}, that is, the target coefficient length is N', N'=N+M.
[0054] Correspondingly, the length of the polyphase coefficients in the polyphase structure representation of an interpolation FIR filter with an interpolation factor of L is: r0(n)={h(0),h(L),h(2L),h(3L),…} r1(n)={h(1),h(L+1),h(2L+1),h(3L+1),…} ... r L-2 (n)={h(L-2),h(2L-2),h(3L-2),h(4L-2),…} r L-1 (n)={h(L-1),h(2L-1),h(3L-1),h(4L-1),…} Thus, by decomposing the target coefficient length into a multiphase structure to obtain the multiphase coefficient length, a lot of unnecessary calculations can be saved during the sampling rate conversion process, thereby greatly improving the calculation speed.
[0055] Furthermore, in this embodiment, step S4 involves adding or subtracting the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure.
[0056] Specifically, in this embodiment, firstly, the i-th phase sub-filter and the L-1-i-th phase sub-filter are taken as two corresponding phase sub-filters, where L represents the number of phase sub-filters; then, the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are added together, and the result is taken as the target polyphase coefficient of the i-th phase sub-filter; and then, the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are subtracted, and the result is taken as the target polyphase coefficient of the L-1-i-th phase sub-filter; finally, the target polyphase coefficients of all phase sub-filters are integrated to obtain a symmetrical combination of coefficients with a symmetrical structure.
[0057] It should be noted that in practical applications, when the number of phase sub-filters is odd, the polyphase coefficients of the new coefficient structure of the (L-1) / 2th phase sub-filter are the target polyphase coefficients of the (L-1) / 2th phase sub-filter, that is, the polyphase coefficients of the intermediate phase phase sub-filters remain unchanged.
[0058] At this point, the target multiphase coefficients can be expressed as: p0(n) = r0(n) + r L-1 (n)={h(0)+h(L-1),h(L)+h(2L-1),h(2L)+h(3L-1),…} p1(n)=r1(n)+r L-2 (n)={h(1)+h(L-2),h(L+1)+h(2L-2),h(2L+1)+h(3L-2),…} ... p L-2 (n)=r L-2 (n)-r1(n)={h(L-2)-h(1),h(2L-2)-h(L+1),h(3L-2)-h(2L+1),…} p L-1 (n)=r L-1 (n)-r0(n)={h(L-1)-h(0),h(2L-1)-h(L),h(3L-1)-h(2L),…} Thus, by adding or subtracting the polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters, the generated target polyphase coefficients have a symmetrical structure, thereby completing phase reorganization.
[0059] Furthermore, in this embodiment, step S5 involves performing symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter.
[0060] Specifically, in this embodiment, the phase sub-filters corresponding to the target polyphase coefficients are such that the i-th (phase) phase sub-filter is positively symmetric, and the L-1-i-th (phase) phase sub-filter is negatively symmetric. Therefore, different processing methods are used for the positively symmetric and negatively symmetric phase sub-filters. The i-th phase sub-filter is operated in pre-addition mode, and the operation process is expressed as follows:
[0061] The L-1-i-th phase sub-filter is operated in pre-decrease mode, and the operation process is expressed as follows:
[0062] Where N represents the original coefficient length and L represents the interpolation factor. This represents the target polyphase coefficient of the i-th phase sub-filter. Indicates the input signal. Let represent the output signal of the i-th phase sub-filter at time n, and k represent the sub-filter coefficient index.
[0063] Thus, the multiphase interpolation FIR filter of arbitrary length possesses symmetry, reducing the number of multiplication operations to N / 2L, significantly reducing multiplier resource consumption. However, the optimized filter coefficients have changed, and the filtering result requires additional computational processing to restore the correct filtering result.
[0064] Furthermore, in this embodiment, step S6 involves recovering the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter.
[0065] Specifically, in this embodiment, the output signal of the i-th phase sub-filter is subtracted from the output signal of the L-1-i-th phase sub-filter, and then multiplied by 1 / 2. The result is used as the filtering result of the i-th phase of the interpolation FIR filter. This process can be expressed as:
[0066] Furthermore, the output signal of the i-th phase sub-filter is added to the output signal of the L-1-i-th phase sub-filter, and then multiplied by 1 / 2. The result is used as the filtering result of the L-1-i-th phase of the interpolation FIR filter. This process can be expressed as:
[0067] Finally, the filtering results of the i-th phase of the interpolated FIR filter and the filtering results of the L-1-i-th phase of the interpolated FIR filter are integrated to obtain the filtering result of the interpolated FIR filter, which can be expressed as:
[0068] The interpolation FIR filter optimization method provided in this embodiment maintains the symmetry of each phase sub-filter by performing zero-placing compensation, polyphase decomposition, and phase reassembly on the interpolation filter coefficients, thereby saving multiplier resources. Furthermore, it restores the output result of the interpolation FIR filter using phase recovery technology, thus optimizing the entire interpolation FIR filtering operation. The optimized polyphase filter structure is shown below. Figure 2 As shown.
[0069] In practical applications, the interpolation FIR filter optimization method provided in this embodiment is compatible with hardware solutions such as ASIC, SOC, and FPGA, and is applicable to multi-channel or sampling application scenarios, with a wide range of applications.
[0070] This embodiment also provides an interpolation FIR filter optimization device for implementing the interpolation FIR filter optimization method described above, such as... Figure 3 As shown, the interpolation FIR filter optimization device includes: The splitting module is used to split the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio; The zero-insertion module is used to perform zero-insertion processing on the original coefficient length based on the relationship between the original coefficient length and the interpolation ratio of the interpolated FIR filter, so as to obtain the target coefficient length. The decomposition module is used to perform multiphase decomposition on the target coefficient length to obtain a new coefficient structure; The arithmetic module is used to perform addition and subtraction operations on the polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure. The folding module is used to perform symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; The recovery module is used to recover the output signal of the phase sub-filter to obtain the filtering result of the interpolated FIR filter.
[0071] The interpolation FIR filter optimization device provided in this embodiment uses a zero-placing module to insert zeros into the coefficient length to meet the coefficient symmetry requirements after polyphase decomposition. This not only effectively reduces the number of interpolation filter multiplication operations by half, but also adapts to arbitrary interpolation ratios and coefficient lengths. The recovery module performs recovery processing on the output signal of each phase sub-filter obtained from the folding module, which can efficiently restore the coefficient phase information and ensure the correctness of the filtering results. This solves the problem of how to reduce the number of FIR filter multiplication operations using a polyphase structure with coefficients of arbitrary length.
[0072] Furthermore, this embodiment also provides an electronic device, including a memory, a processor, and an executable program stored in the memory and capable of being run by the processor; when the processor runs the executable program, it performs the interpolation FIR filter optimization method as described above.
[0073] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to mutually. In addition, different parts between embodiments can also be combined with each other, and this invention does not limit this.
[0074] This embodiment provides an interpolation FIR filter optimization method, apparatus, and electronic device, comprising: decomposing the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio; performing zero-placing on the original coefficient length according to the relationship between the original coefficient length of the interpolation FIR filter and the interpolation ratio to obtain a target coefficient length; performing polyphase decomposition on the target coefficient length to obtain a new coefficient structure; performing addition and subtraction operations on the polyphase coefficients of the new coefficient structures of corresponding two phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure; performing symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; and performing recovery processing on the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter. By performing zero-placing on the coefficient length to meet the coefficient symmetry requirements after polyphase decomposition, not only can the number of interpolation filtering multiplication operations be effectively reduced by half, but it can also adapt to arbitrary interpolation ratios and coefficient lengths; by performing recovery processing after obtaining the output signal of each phase sub-filter, the coefficient phase information can be efficiently restored, ensuring the correctness of the filtering result, and solving the problem of how to reduce the number of FIR filter multiplication operations using a polyphase structure with coefficients of arbitrary length.
[0075] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.
Claims
1. An interpolation FIR filter optimization method, characterized by, include: Based on the interpolation factor, the interpolation FIR filter is divided into multiple phase sub-filters, including: based on the interpolation factor L, the interpolation FIR filter is divided into L phase sub-filters; Based on the relationship between the original coefficient length and the interpolation ratio of the interpolated FIR filter, the original coefficient length is zero-placing to obtain the target coefficient length. The target coefficient length is decomposed into multiple phases to obtain a new coefficient structure; The polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters are added or subtracted to obtain a symmetrical combination of coefficients with a symmetrical structure, wherein the i-th phase sub-filter and the L-1-i-th phase sub-filter are regarded as the two corresponding phase sub-filters. Symmetrical folding is performed on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter, including: The i-th phase sub-filter is operated in pre-addition mode, and the operation process is expressed as follows: The L-1-i-th phase sub-filter is operated in pre-decrease mode, and the operation process is expressed as follows: Where N represents the original coefficient length and L represents the interpolation factor. This represents the target polyphase coefficient of the i-th phase sub-filter. Indicates the input signal. Let represent the output signal of the i-th phase sub-filter at time n, and k represent the sub-filter coefficient index; The output signal of the phase sub-filter is recovered to obtain the filtering result of the interpolation FIR filter.
2. The interpolation FIR filter optimization method according to claim 1, characterized in that, All of the phase sub-filters have the same length.
3. The interpolation FIR filter optimization method according to claim 1, characterized in that, The method for obtaining the target coefficient length by zero-placing the original coefficient length based on the relationship between the original coefficient length of the interpolated FIR filter and the interpolation ratio includes: If the original coefficient length cannot be divided evenly by the interpolation factor, then zero-placing is performed on the original coefficient length to obtain the target coefficient length; Otherwise, the original coefficient length is used directly as the target coefficient length.
4. The interpolation FIR filter optimization method according to claim 3, characterized in that, The method for inserting zeros into the original coefficient length to obtain the target coefficient length if the original coefficient length cannot be divided evenly by the interpolation factor includes: If the interpolation factor is even and the original coefficient length is odd-symmetric, then an odd number of zero values are inserted into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor. Otherwise, insert an even number of zero values into the original coefficient length to compensate for the original coefficient length, so that the compensated target coefficient length can be divided by the interpolation factor.
5. The interpolation FIR filter optimization method according to claim 4, characterized in that, The number of odd-number zero values inserted into the original coefficient length is: Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. Indicates rounding up; The number of zero values inserted at the beginning of the original coefficient length is M / 2, and the number of zero values inserted at the end of the original coefficient length is (M+1) / 2.
6. The interpolation FIR filter optimization method according to claim 4, characterized in that, The number of even-number zero values inserted into the original coefficient length is: Where M represents the number of zero values inserted, N represents the original coefficient length, and L represents the interpolation factor. Indicates rounding down; The number of zero values inserted at the beginning and end of the original coefficient length is M / 2, respectively.
7. The interpolation FIR filter optimization method according to claim 1, characterized in that, The method of adding or subtracting the polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure includes: The i-th phase sub-filter and the L-1-i-th phase sub-filter are regarded as two corresponding phase sub-filters, where L represents the number of phase sub-filters; The polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are added together, and the result is used as the target polyphase coefficient of the i-th phase sub-filter. The polyphase coefficients of the new coefficient structures of the two corresponding phase sub-filters are subtracted, and the result is used as the target polyphase coefficient of the L-1-i-th phase sub-filter. Integrate the target polyphase coefficients of all phase sub-filters to obtain a coefficient symmetric combination with a symmetric structure.
8. The interpolation FIR filter optimization method according to claim 7, characterized in that, The method of adding or subtracting the polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters to obtain the target polyphase coefficient length of the symmetrical structure further includes: When the number of phase sub-filters is odd, the polyphase coefficients of the new coefficient structure of the (L-1) / 2th phase sub-filter are the target polyphase coefficients of the (L-1) / 2th phase sub-filter.
9. The interpolation FIR filter optimization method according to claim 1, characterized in that, The method for recovering the output signal of the phase sub-filter to obtain the filtering result of the interpolation FIR filter includes: The output signal of the i-th phase sub-filter is subtracted from the output signal of the L-1-i-th phase sub-filter and then multiplied by 1 / 2. The result is used as the filtering result of the i-th phase of the interpolation FIR filter. The output signal of the i-th phase sub-filter is added to the output signal of the L-1-i-th phase sub-filter and then multiplied by 1 / 2. The result is used as the filtering result of the L-1-i-th phase of the interpolation FIR filter. The filtering results of the i-th phase of the interpolated FIR filter and the filtering results of the L-1-i-th phase of the interpolated FIR filter are integrated to obtain the filtering result of the interpolated FIR filter.
10. An interpolation FIR filter optimization apparatus, used to implement the interpolation FIR filter optimization method as described in any one of claims 1 to 9, characterized in that, The interpolation FIR filter optimization device includes: The splitting module is used to split the interpolation FIR filter into multiple phase sub-filters according to the interpolation ratio; The zero-insertion module is used to perform zero-insertion processing on the original coefficient length based on the relationship between the original coefficient length and the interpolation ratio of the interpolated FIR filter, so as to obtain the target coefficient length. The decomposition module is used to perform multiphase decomposition on the target coefficient length to obtain a new coefficient structure; The arithmetic module is used to perform addition and subtraction operations on the polyphase coefficients of the new coefficient structure of the two corresponding phase sub-filters to obtain a symmetrical combination of coefficients with a symmetrical structure. The folding module is used to perform symmetrical folding on the symmetrical combination of coefficients to obtain the output signal of each phase sub-filter; The recovery module is used to recover the output signal of the phase sub-filter to obtain the filtering result of the interpolated FIR filter.
11. An electronic device, characterized in that, It includes a memory, a processor, and an executable program stored in the memory and capable of being run by the processor; when the processor runs the executable program, it performs the interpolation FIR filter optimization method as described in any one of claims 1 to 9.