0 Preface
Adaptive filters have been widely used in various aspects such as channel equalization, echo cancellation, system identification, and spectrum estimation. Adaptive filtering based on subband decomposition improves the convergence performance while saving a certain amount of calculation. The adaptive filtering based on subband decomposition firstly divides the input signal and the reference signal through the decomposition filter bank to perform subband decomposition, extraction, subband adaptive filtering, interpolation, and obtains the output signal through the synthesis filter bank. The advantages of an adaptive filter based on subband decomposition:
(1) Due to the extraction of the signal, the amount of calculation required to complete adaptive filtering can be reduced;
(2) Adaptive filtering in subbands improves the convergence performance.
1 Adaptive filtering structure based on subband decomposition
The adaptive filtering based on subband decomposition, its time domain structure is shown in Figure 1. Sub-band decomposition and extraction of the input signal x (n) and the reference signal d (n), adaptive filtering on the sub-band, and then the estimated signals y0 (n) and y1 (n) on the sub-band Interpolate and synthesize the filter bank to get the final synthesized signal. The filters W00 (n) and W11 (n) are adaptive filters on the two subbands, while W01 (n) and W10 (n) represent the adaptive filters between subbands. This is because the filter banks are all FIR filters, and it is impossible to have the ideal characteristics of sharp cut-off. Only the cost can be exchanged for the approximate characteristics; at this time, the subband signals obtained under strict sampling must have aliasing, which requires Add inter-subband filtering to eliminate its effects. The subband adaptive filter here uses an adaptive filter based on the NLMS algorithm. The NLMS algorithm is compared with the LMS algorithm. Although the amount of calculation is slightly increased, the convergence speed of the adaptive filter can be greatly improved.
2 Design of dual-channel filter bank
The relationship between the analysis and synthesis filters used in this article is as follows:
H1 (z) = H0 (-z), G1 (z) =-2H0 (-z), G0 (z) = 2H1 (-z). It can be seen from the above expression that the key to design is to design H0 (z), as long as H0 (z) is determined, H1 (z), G0 (z), and G1 (z) can also be determined. This paper adopts equal ripple approach design method to filter design. The filter designed by this method exhibits equal ripple frequency response. The filter designed by the equal ripple approach design method has the following advantages:
(1) Since the error is evenly distributed over the entire frequency band, for a fixed order N, the best filtering characteristics can be obtained;
(2) The passband is the flattest, and the minimum attenuation of the stopband reaches the maximum.
Matlab integrates a powerful set of filter design tools FDATOOL, which can complete the design, analysis and performance evaluation of various filters. The frequency characteristic curve of 4 FIR filters used in FPGA hardware realization part of this text is shown in Fig. 2.
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