A method, system, apparatus, and medium for designing a quasi-perfect reconstruction filter bank

Abstract

This invention relates to the field of filter technology, and particularly to a design method, system, device, and medium for a quasi-completely reconstructed filter bank. The method first uses a generalized monotonic asymptotically saturated function as the initial value of a prototype filter, substituting it into the filter bank model for optimization to obtain a baseline fully reconstructed prototype filter. Then, a transition band adjustment parameter is introduced to perform an analytical mapping transformation on the amplitude-frequency response of the baseline fully reconstructed prototype filter, resulting in a fully reconstructed prototype filter with optimized transition band. Finally, combined with a determined number of filter bank channels and the polyphase decomposition length of the prototype filter, a quasi-completely reconstructed prototype filter is obtained through frequency domain sampling and transformation processing, which is then modulated to obtain a quasi-completely reconstructed filter bank. This method, by introducing a generalized monotonic asymptotically saturated function as the initial value of the prototype filter and combining it with the analytical mapping mechanism of the transition band adjustment parameter, significantly improves stopband attenuation performance and increases the efficiency of prototype filter coefficient generation while ensuring quasi-complete reconstruction.

Description

Technical Field

[0001] This invention relates to the field of filter technology, and in particular to a design method, system, device and medium for a quasi-completely reconstructable filter bank. Background Technology

[0002] With the development of modern communication and electronic reconnaissance technologies, channelizers, as the core components of broadband digital transmission and reception, are widely used in broadband digital signal processing scenarios. Filter bank-based channelization structures have become the mainstream scheme for realizing broadband signal frequency division and synthesis due to their efficient various polyphase implementation structures. In these applications, the design quality of the filter bank prototype filter directly determines the performance of the channelizer. The prototype filter is required to have high stopband attenuation to suppress aliasing, while satisfying the complete reconstruction condition to eliminate amplitude distortion.

[0003] Existing technologies for designing such prototype filters mainly include the PM algorithm, window function method, pseudo-orthogonal mirror filter method, and iterative algorithms based on optimization criteria (such as the Remez exchange algorithm). While the window function method is simple, its stopband attenuation and transition band width are strongly coupled and difficult to control independently. Optimization algorithms, although achieving good filtering performance, typically involve complex iterative search processes, resulting in high computational costs and difficulty in establishing a direct analytical relationship between design parameters and filter coefficients. Therefore, for prototype filter design tasks with a small number of channels and low order, the shortcomings of existing methods can be ignored. However, when the required number of channelization channels is large, for prototype filter design tasks of tens of thousands of orders, some algorithms are no longer sufficient. These shortcomings become key bottlenecks in improving the performance of channelizer design. This type of existing technology has the following drawbacks: (1) High design difficulty: Most of the existing technologies mentioned above take the filter order or stopband characteristics as the main design goal and fail to incorporate the quasi-complete reconstruction requirement as a design constraint into the unified design process. Therefore, in order to meet multiple performance indicators such as filter order, stopband characteristics and quasi-complete reconstruction at the same time, it is often necessary to repeatedly weigh and adjust multiple parameters, resulting in high design difficulty. (2) High computational overhead: The existing technologies mentioned above generally adopt numerical design methods that rely on multiple iterative searches, which require the construction of a large constraint matrix and repeated solving of quadratic programming or linear equation systems, resulting in high computational overhead; when the filter order is high or the performance requirements are strict, the convergence speed is slow and the stable solution cannot be guaranteed. (3) Poor flexibility of the scheme: The existing technologies mentioned above usually indirectly affect the filter characteristics by adjusting the weighting coefficients or order, and lack a design mechanism for direct and analytical control of key parameters such as transition band width; therefore, when the system indicators are adjusted, it is often necessary to re-execute the complete design and solution process, resulting in poor scheme flexibility. Chinese patent CN105677957B discloses a design method for an approximately accurate reconstruction cosine modulation filter bank. This method calculates the prototype filter coefficients by establishing a mathematical model with the goal of minimizing stopband energy and with approximately accurate reconstruction conditions as constraints; however, this method relies on the iterative solution of a non-convex optimization problem. This method is relatively effective when the filter order is low, but when the filter order reaches tens of thousands, it requires a large computational overhead and may not converge.

[0004] Chinese patent CN106712836B discloses a channelizer design method based on an approximately accurate reconstruction filter bank. This method introduces a reconstruction performance relaxation parameter to characterize the required reconstruction error performance. By optimizing the model, the order of the filter is reduced while meeting the reconstruction error requirements. However, its stopband attenuation is relatively low, and the filter bank splicing error (peak-to-peak value) is relatively high. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to propose a design method, system, device and medium for a quasi-completely reconstructed filter bank. This method is based on the analytical characteristics of the generalized monotonic asymptotic saturation function and achieves precise control of the filter characteristics by adjusting the transition band parameters. It solves the technical problems in the existing channelizer filter bank design method, where the prototype filter design is difficult to simultaneously take into account high stopband attenuation, low splicing error and insufficient design flexibility.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Firstly, a design method for a quasi-completely reconstructed filter bank includes the following steps: S1. Based on the determined number of channels in the filter bank Length of polyphase decomposition of prototype filter By combining the criterion of minimizing the total stopband energy, a mathematical model of the filter bank that satisfies the complete reconstruction constraint is established, and the generalized monotonic asymptotic saturation function is applied. Substituting the initial values ​​of the prototype filter into the mathematical model of the filter bank for optimization, a baseline fully reconstructed prototype filter that satisfies the conditions for complete reconstruction is obtained. ; S2. Introduce the transition band adjustment parameters of the prototype filter. Without violating the power complementarity constraint, the prototype filter is completely reconstructed from the reference. Amplitude-frequency response Perform an analytical mapping transformation to obtain the fully reconstructed prototype filter with optimized transition band. ; S3. Based on the number of channels of the filter bank described in step S1 Length of polyphase decomposition of prototype filter The fully reconstructed prototype filter after transition band optimization described in step S2 By frequency domain sampling and transformation processing, a quasi-completely reconstructed prototype filter is obtained. For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank; Among them, the generalized monotone asymptotic saturation function mentioned in step S1 It satisfies the conditions of being centrally symmetric, monotonic in its domain, and asymptotically convergent to two different constants.

[0007] Furthermore, the transition band adjustment parameter K of the prototype filter in step S1 is a constant, and the fully reconstructed prototype filter after transition band optimization in step S2... Amplitude-frequency response satisfy: ,in for The amplitude-frequency response obtained by performing a Fourier transform. Amplitude-frequency response The half-power point frequency at the edge of the passband.

[0008] Further, the number of channels of the filter bank described in step S1 The actual number of subbands under cosine modulation, and the number of channelized subbands under complex modulation. The generalized monotone asymptotic saturation function described in step S1 A typical implementation of this is the error function (erf).

[0009] Furthermore, step S2 includes the following sub-steps: S21: Based on the power complementarity characteristics, the reference fully reconstructed prototype filter described in step S1 is obtained. frequency response Half-power point frequency at the passband edge The half-power point frequency satisfy ; S22: Introduce the transition band adjustment parameters of the prototype filter described in step S1. Satisfying amplitude-frequency response The fully reconstructed prototype filter after transition band optimization is obtained. .

[0010] Furthermore, step S3 includes the following sub-steps: S31: Based on the number of channels of the filter bank described in step S1 Length of polyphase decomposition of prototype filter The fully reconstructed prototype filter after transition band optimization in step S2 is applied within the normalized frequency range. Discrete downsampling is performed, and the spectrum is extended to the full bandwidth based on conjugate symmetry to obtain the target standard fully reconstructed prototype filter spectrum sequence. ; S32: Completely reconstruct the prototype filter spectrum sequence according to the target standard described in step S31. Perform the inverse discrete Fourier transform (IDFT), followed by cyclic shifting and windowing truncation, to obtain a length of... Quasi-complete reconstruction prototype filter For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank.

[0011] Secondly, a system based on the design method of the quasi-complete reconstruction filter bank includes the following modules: Reference prototype filter generation module: Based on the determined number of channels in the filter bank Length of polyphase decomposition of prototype filter By combining the criterion of minimizing the total stopband energy, a mathematical model of the filter bank that satisfies the complete reconstruction constraint is established, and the generalized monotonic asymptotic saturation function is applied. Substituting the initial values ​​of the prototype filter into the mathematical model of the filter bank for optimization, a baseline fully reconstructed prototype filter that satisfies the conditions for complete reconstruction is obtained. ; wherein, the generalized monotone asymptotic saturation function It satisfies the conditions of being centrally symmetric, monotonic in its domain, and asymptotically convergent to two different constants; Transition band resolution control module: Introduces the transition band adjustment parameters of the prototype filter. Without violating the power complementarity constraint, the prototype filter is completely reconstructed from the reference. An analytical mapping transformation is performed on the amplitude-frequency response to obtain the fully reconstructed prototype filter with optimized transition band. ; Prototype filter reconstruction module: Based on the number of channels of the filter bank Length of polyphase decomposition of prototype filter With the fully reconstructed prototype filter optimized for the transition band By frequency domain sampling and transformation processing, a quasi-completely reconstructed prototype filter is obtained. For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank.

[0012] Thirdly, an electronic device includes the quasi-complete reconstruction filter bank; for example, a channelizer, a transparent repeater, or a filter bank multicarrier modulator constructed based on the quasi-complete reconstruction filter bank. The quasi-complete reconstruction prototype filter generated by this invention... The quasi-complete reconstruction filter bank is universal, protecting the prototype filter based on this quasi-complete reconstruction. Various types of filter banks and channelizers were constructed, including but not limited to complex exponential modulation (DFT filter bank), cosine modulation (CMFB), and improved cosine modulation (MDFT).

[0013] Fourthly, a computer-readable storage medium stores a computer program that, when executed by a processor, implements the design method of the quasi-complete reconstruction filter bank; the computer-readable storage medium includes various media capable of storing program code, such as a USB flash drive, read-only memory (ROM), random access memory (RAM), portable hard disk, magnetic disk, or optical disk.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: This method can solve the following core technical problems existing in the design of current broadband digital channelized receivers: (1) Unlike existing technologies that typically use random initial values, ideal rectangular windows, or traditional window functions as the starting point for optimization, this method proposes in step S1 to use a class of generalized functions (such as error functions, hyperbolic tangent functions, etc.) that have monotonic, continuous, and asymptotically convergent characteristics to two different finite constants as the initial value of the prototype filter. These functions naturally have low-pass characteristics and smooth transition bands in the frequency domain. Substituting them as initial values ​​into the optimization model can significantly accelerate convergence and avoid getting trapped in local optima.

[0015] (2) In step S2 of this method, an analytical mapping formula is proposed that can directly control the transition band characteristics of the prototype filter, so as to completely reconstruct the half-power point of the prototype filter based on the benchmark. Using anchor points, the power complementarity characteristic is always satisfied during deformation, ensuring that the quasi-complete reconfiguration condition is not violated; through a single parameter The transition band characteristics of the prototype filter can be continuously adjusted without resolving complex optimization equations, which greatly improves the flexibility of engineering applications.

[0016] In summary, this method introduces a specific analytic function, namely the generalized monotonic asymptotic saturation function. As the initial value of the prototype filter that satisfies the complete reconstruction constraint, and combined with the analytical mapping mechanism of the transition band adjustment parameter K, the stopband attenuation performance is significantly improved while ensuring the quasi-complete reconstruction characteristics. The solution complexity of the traditional numerical design process of multiple iterations is greatly reduced, the computational complexity is significantly reduced while ensuring the controllability of design indicators, the generation efficiency of prototype filter coefficients is improved, and flexible and precise control of prototype filter characteristics is achieved. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the method.

[0018] Figure 2(a) shows the amplitude-frequency response curve of the prototype filter in Example 1.

[0019] Figure 2(b) shows the amplitude splicing jitter curve of the filter bank in Example 1.

[0020] Figure 3 This is a schematic diagram of the channelizer analysis structure in Example 1.

[0021] Figure 4 This is a schematic diagram of the integrated structure of the channelizer in Embodiment 1.

[0022] Figure 5(a) shows the amplitude-frequency response curve of the prototype filter constructed using the error function in Example 2.

[0023] Figure 5(b) shows the amplitude splicing jitter curve of the filter bank constructed by the error function in Example 2.

[0024] Figure 6(a) shows the amplitude-frequency response curve of the prototype filter constructed using the Logistic function in Example 2.

[0025] Figure 6(b) shows the amplitude splicing jitter curve of the filter bank constructed by the Logistic function in Example 2.

[0026] Figure 7(a) shows the amplitude-frequency response curve of the prototype filter constructed by improving the arctangent function in Example 2.

[0027] Figure 7(b) shows the amplitude splicing jitter curve of the filter bank constructed by the improved arctangent function in Example 2. Detailed Implementation

[0028] The following is in conjunction with the appendix Figure 1 The invention will be further described in detail with reference to Figure 7(b): Several points regarding the design method of the quasi-complete reconstruction filter bank in this invention: 1. Generalized monotone asymptotically saturated function Function family replacement The embodiments in this specification use an improved error function (erf) as an example to illustrate the role of a generalized monotonic asymptotically saturated function. However, any generalized monotonic asymptotically saturated function that satisfies the "S-curve" characteristic (Sigmoid-like functions) can be substituted, including but not limited to: Logistic function, arctangent function, hyperbolic tangent function, algebraic function, smooth step function, etc.

[0029] 2. A variant of the frequency domain analytical mapping mechanism for the transition band adjustment parameter K. This invention achieves transition bandwidth control through a frequency domain analytical mapping mechanism of the transition band adjustment parameter K. It also includes a nonlinear relationship to replace the current linear K-fold stretching, as long as the objective is to maintain... Changing the steepness of the transition zone without altering the underlying conditions constitutes an equivalent substitution in this invention.

[0030] 3. The filter bank designed in this invention can be applied to different hardware, including but not limited to: Computing platform: The channelizer can be implemented on FPGA, ASIC, DSP, GPU or general-purpose CPU; Application architecture: The filter bank can be a polyphase filter structure or a direct FIR structure, and the channelizer can be a complex exponential modulation (DFT filter bank), cosine modulation (CMFB), improved DFT modulation (MDFT) structure, etc. Coefficient storage: Filter coefficients can be pre-calculated and stored in ROM / RAM, or they can be generated in real time by software during system power-on initialization.

[0031] Example 1 Take in step S1 Take the polyphase decomposition length of the filter The error function is taken as the generalized monotone asymptotic saturation function. ,satisfy It asymptotically converges between constants -1 and 1, and the transition band adjustment parameter is taken. .

[0032] In step S1, the mathematical model for the fully reconstructed filter bank that minimizes the total stopband energy is established as follows: Here, "min" and "st" are mathematical programming terms, representing "minimization" and "constraints," respectively; objective function The design objective is to minimize the energy of the prototype analysis filter in the stopband frequency range; constraints. This represents the complete reconstruction condition that must be satisfied during the prototype analysis filter design process. Let be the coefficient vector, where Represents the length of the prototype filter; For the stopband energy matrix, For the constraint matrix, represent 3D complex vector Represents conjugate transpose. The formula is as follows: in This is the shift matrix used to extract the correlation coefficient.

[0033] In step S2, based on the power complementarity characteristics of the fully reconfigured filter, the following steps are performed: Perform a Fourier transform to calculate the half-power point frequency of its amplitude response at the edge of the passband. ,satisfy Filter transition band adjustment parameters Constructing a new amplitude-frequency response ,satisfy: By adjusting The value can be adjusted to achieve the target design performance while maintaining the near-complete reconfiguration characteristics.

[0034] In step S3, based on the number of channels in the filter bank Length of polyphase decomposition of prototype filter The prototype filter length is obtained. As a frequency sample value, within the normalized frequency range Discrete sampling is performed, and the spectrum sequence is obtained by extending it to the entire frequency band based on conjugate symmetry. After performing the inverse discrete Fourier transform (IDFT) and applying cyclic shifting and windowing, a length of [length missing] is obtained. Real-domain filter coefficients Its amplitude-frequency response curve and the reconstruction performance curve of the filter bank it forms are shown in Figure 2(a) and Figure 2(b).

[0035] use Complex exponential modulation is performed to generate an analysis filter bank. and synthesis filter bank Used for channelizer design, thereby achieving attached Figure 3 Appendix Figure 4 The quasi-complete reconstruction filter bank channelizer shown.

[0036] Example 1 is used to target The simulation scenario was designed and compared with existing technologies. The simulation results are shown in Table 1 below: Table 1 Comparison of Simulation Results between Example 1 and Existing Technologies As can be seen from the data, while keeping the filter order and computational complexity unchanged, the stopband attenuation of the prototype filter designed in this embodiment is improved by about 30dB, which greatly enhances the anti-aliasing capability; and the peak-to-peak splicing error is reduced by about 20%, which significantly improves the signal separation capability and reconstruction quality of the channelizer and ensures higher signal fidelity.

[0037] Example 2 As shown in Figures 5(a) to 7(b), Example 2 demonstrates the performance comparison of the designed filters when different generalized monotonic asymptotic saturation functions are used as the initial values ​​of the prototype filters.

[0038] Select error functions respectively The Logistic function converges between -1 and 1. And an improved arctangent function The values ​​converge to between -π / 2 and π / 2, which are used as initial values ​​for the filter to satisfy the complete reconstruction constraint. These initial values ​​are then substituted into the established mathematical model of the filter bank for optimization. The simulation results are compared and shown in Table 2 below. Table 2. Comparison of the effects of different generalized monotonic asymptotic saturation functions as initial values ​​for prototype filters. The working principle of this invention is as follows: In this invention, a generalized monotonic asymptotic saturation function is first used as the initial function of the amplitude-frequency response of the prototype filter. This function is then substituted into the mathematical model of the filter bank that minimizes the total stopband energy criterion for optimization, thereby obtaining a benchmark fully reconstructed prototype filter that satisfies the full reconstruction condition. Subsequently, the half-power point frequency of the prototype filter is determined, and a transition band adjustment parameter is introduced to perform a frequency mapping transformation on the frequency response of the prototype filter. This allows for controllable adjustment of the transition band width while maintaining the power complementarity relationship. Finally, a quasi-fully reconstructed prototype filter and its corresponding filter bank are obtained through frequency domain sampling and inverse discrete Fourier transform, thus enabling the rapid design of high-order filters while avoiding complex iterative optimization calculations.

Claims

1. A method of designing a quasi-perfect reconstruction filter bank, characterized by, Includes the following steps: S1. Based on the determined number of channels in the filter bank Length of polyphase decomposition of prototype filter By combining the criterion of minimizing the total stopband energy, a mathematical model of the filter bank that satisfies the complete reconstruction constraint is established, and the generalized monotonic asymptotic saturation function is applied. Substituting the initial values ​​of the prototype filter into the mathematical model of the filter bank for optimization, a baseline fully reconstructed prototype filter that satisfies the conditions for complete reconstruction is obtained. The generalized monotone asymptotic saturation function It satisfies the conditions of being centrally symmetric, monotonic in its domain, and asymptotically convergent to two different constants; S2. Introduce the transition band adjustment parameters of the prototype filter described in step S1. Without violating the power complementarity constraint, the prototype filter described in step S1 is completely reconstructed. Amplitude-frequency response Perform an analytical mapping transformation to obtain the fully reconstructed prototype filter with optimized transition band. ; S3. Based on the number of channels of the filter bank described in step S1 Length of polyphase decomposition of prototype filter The fully reconstructed prototype filter after transition band optimization described in step S2 By frequency domain sampling and transformation processing, a quasi-completely reconstructed prototype filter is obtained. For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank.

2. The design method of a quasi-complete reconstruction filter bank as described in claim 1, characterized in that, The transition band adjustment parameter K of the prototype filter is a constant, and the fully reconstructed prototype filter after transition band optimization... Amplitude-frequency response satisfy: in for The amplitude-frequency response obtained by performing a Fourier transform. Amplitude-frequency response The half-power point frequency at the edge of the passband.

3. The design method of a quasi-completely reconstructed filter bank as described in claim 1, characterized in that, The number of channels of the filter bank in step S1 The actual number of subbands under cosine modulation, and the number of channelized subbands under complex modulation. The generalized monotone asymptotic saturation function described in step S1 This is the error function.

4. The design method of a quasi-complete reconstruction filter bank as described in claim 1, characterized in that, Step S2 includes the following sub-steps: S21: Based on the power complementarity characteristics, the reference fully reconstructed prototype filter described in step S1 is obtained. frequency response Half-power point frequency at the passband edge The half-power point frequency satisfy ; S22: Introduce the transition band adjustment parameters of the prototype filter described in step S1. Satisfying amplitude-frequency response The fully reconstructed prototype filter after transition band optimization is obtained. .

5. The design method of a quasi-completely reconstructed filter bank as described in claim 1, characterized in that, Step S3 includes the following sub-steps: S31: Based on the number of channels of the filter bank described in step S1 Length of polyphase decomposition of prototype filter The fully reconstructed prototype filter after transition band optimization in step S2 is applied within the normalized frequency range. Discrete downsampling is performed, and the spectrum is extended to the full bandwidth based on conjugate symmetry to obtain the target standard fully reconstructed prototype filter spectrum sequence. ; S32: Completely reconstruct the prototype filter spectrum sequence according to the target standard described in step S31. Perform the inverse discrete Fourier transform (IDFT), followed by cyclic shifting and windowing truncation, to obtain a length of... Quasi-complete reconstruction prototype filter For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank.

6. A system based on the design method of the quasi-complete reconstruction filter bank according to any one of claims 1 to 5, characterized in that, Includes the following modules: Reference prototype filter generation module: Based on the determined number of channels in the filter bank Length of polyphase decomposition of prototype filter By combining the criterion of minimizing the total stopband energy, a mathematical model of the filter bank that satisfies the complete reconstruction constraint is established, and the generalized monotonic asymptotic saturation function is applied. Substituting the initial values ​​of the prototype filter into the mathematical model of the filter bank for optimization, a baseline fully reconstructed prototype filter that satisfies the conditions for complete reconstruction is obtained. ; wherein, the generalized monotone asymptotic saturation function It satisfies the conditions of being centrally symmetric, monotonic in its domain, and asymptotically convergent to two different constants; Transition band resolution control module: Introduces the transition band adjustment parameters of the prototype filter. Without violating the power complementarity constraint, the prototype filter is completely reconstructed from the reference. An analytical mapping transformation is performed on the amplitude-frequency response to obtain the fully reconstructed prototype filter with optimized transition band. ; Prototype filter reconstruction module: Based on the number of channels of the filter bank Length of polyphase decomposition of prototype filter With the fully reconstructed prototype filter optimized for the transition band By frequency domain sampling and transformation processing, a quasi-completely reconstructed prototype filter is obtained. For the quasi-completely reconstructed prototype filter Cosine or complex exponential modulation is applied to obtain a quasi-completely reconstructed filter bank.

7. An electronic device, characterized in that, Includes the quasi-complete reconstruction filter bank as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the design method of the quasi-completely reconstructed filter bank as described in any one of claims 1 to 5.

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