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Design method of separable two-dimensional FIR filter with sparse coefficient

A technique of sparse coefficients, design methods, applied in computer-aided design, design optimization/simulation, instrumentation, etc.

Active Publication Date: 2019-10-22
HANGZHOU DIANZI UNIV
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Problems solved by technology

Solving the sparse solution is essentially a 0-norm maximization problem, but this is an NP-Hard problem

Method used

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  • Design method of separable two-dimensional FIR filter with sparse coefficient
  • Design method of separable two-dimensional FIR filter with sparse coefficient
  • Design method of separable two-dimensional FIR filter with sparse coefficient

Examples

Experimental program
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Effect test

example 1

[0119] Example 1. Design a quarter-symmetric circular two-dimensional FIR filter, the ideal frequency response is as follows:

[0120]

[0121] where ω p = 0.5 π, ω s =0.7·π, the order of the filter is N=11×11, 17×17, 23×23 and 29×29 respectively, N 1 and N 2 satisfy For different orders, the number of frequency sampling points Γ is 1521, 1521, 1521 and 1225 in turn; the value of K is 4, 5, 5 and 6 in turn. The parameter ε=0.15 in step 2, and the number of iterations is 10. The parameter ε of step 3 cof_bound =0.0001, the parameter σ=0.0001, and the number of iterations is 15. For filters with different orders, the number of iterations in step five is 3, 1, 4 and 2 in sequence. Table 1 shows the results of the designed separable FIR circular filter with sparse coefficients and the corresponding design parameters. The frequency response is shown in Figure 3(a)-(d);

[0122] Table 1 Design results of separable two-dimensional FIR circular sparse filter

[0123]

...

example 2

[0125] Example 2. Design a quarter-symmetric diamond-shaped two-dimensional FIR filter. The ideal frequency response is as follows:

[0126]

[0127] where ω p =0.6·π,ω s =π, the order of the filter is N=11×11, 17×17, 23×23 and 29×29 respectively, N 1 and N 2 satisfy For different orders, the number of frequency sampling points Γ takes values ​​1521, 1521, 1521 and 1521 in turn; the values ​​of K are 5, 5, 5 and 6 in turn. The parameter ε=0.15 in step 2, and the number of iterations is 10. The parameter ε of step 3 cof_bound =0.0001, the parameter σ=0.0001, and the number of iterations is 15. For filters of different orders, the number of iterations in step five is 2, 4, 1 and 1 in turn. Table 2 shows the results of the designed separable FIR diamond filter with sparse coefficients and the corresponding design parameters. The frequency response is shown in Figure 4(a)-(d);

[0128] Table 2 Design results of separable two-dimensional FIR diamond sparse filter

[0...

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Abstract

The invention provides a design method of a separable two-dimensional FIR filter with a sparse coefficient, and relates to a sparse algorithm combining an iterative reweighted l1 norm and a greedy search technology. The design method is different from a conventional method as the design method uses a sparse algorithm in the design of the separable two-dimensional FIR filter for the first time, wherein since the frequency response function of the separable two-dimensional FIR filter is a non-convex problem, and the l1 norm method cannot be directly applied, the design method solves the problemby fixing some coefficients and maximizing the number of zero coefficients in the rest coefficients at the same time. The design method has the advantages that the hardware complexity for realizing the two-dimensional FIR filter is reduced; the signal processing efficiency is improved; and the trust region iterative gradient search technology is fused in the design process, so that the coefficientof the filter is more accurate, and the obtained performance index of the filter has more superiority.

Description

technical field [0001] The invention belongs to the technical field of digital signal processing, in particular to an iterative reweighting based Design method of separable two-dimensional FIR sparse filter combined with norm and greedy search technique. Background technique [0002] As an important part of two-dimensional digital signal processing, two-dimensional FIR digital filter has been widely used in many aspects such as medical image processing, satellite image processing, radar, sonar and seismic signal processing. However, the two-dimensional FIR filter has significant disadvantages of high hardware implementation complexity (the hardware implementation complexity of the FIR filter is usually measured by the number of multipliers and adders required for hardware implementation) and high group delay, especially when the frequency of the digital filter is high. When the domain performance requirements are high, the problem of high hardware implementation complexity...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03H17/06G06F17/50
CPCH03H17/06H03H2017/0081G06F30/20
Inventor 王浩李伟琪赵知劲赵晨子李祥振靳一
Owner HANGZHOU DIANZI UNIV
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