Design of IIR-based wavelet filter banks and their application to image coding

Abstract

The two -channel QMF filter bank based on allpass sections is one of the best known circuits for building up a multi -channel filter bank for signal compression. An analysis -synthesis combination can satisfy two of the three PR conditions. The third, phase condition, can be met to any desired accuracy. In this contribution, we consider the development of explicit formulae for the coefficients of such filters. The resulting QMF designs can be used in a wavelet structure for image compression problems using separable filters or Ansari and Lau's method. Several design examples are given including a comparison of performance with FIR filter banks for such problems.

Neural network‐based design of 2‐channel quadrature mirror filter banks

“…11,12,15,25,26 Two neural networks with different number of neurons and Hopfield-related parameters are concurrently designed to obtain the IIR all-pass filters a 1 (n) and a 2 (n). To evaluate the design performance of the proposed neural-based method, the all-pass-based QMF bank designs set the same specifications as those of methods.…”

“…Two Hopfield neural networks (shown in Figure 3) run 5μs to approximate the convergence of the dynamic states v 1,n and v 2,n which correspond to the all-pass filter coefficients a 1 (n) and a 2 (n), respectively. 11,15 Figure 5B, C depicts that FIGURE 3 The design of IIR all-pass-based QMF banks using Hopfield neural network (i = 1, 2) the proposed neural-based approach has smaller phase error and group delay error responses than methods. 15 Obviously, the magnitude responses of the designed analysis filters achieve good low-pass and high-pass characteristics as shown in Figure 5A.…”

“…Figure 5 demonstrates the results designed by the proposed neural-based method, Lawson's method, 11 and Lee and Yang method. 11,15 The designed magnitude error response of QMF banks surpasses those of methods 11,15 which can be seen from Figure 5D. The presented approach yields excellent stopband attenuation than methods.…”

“…The presented approach yields excellent stopband attenuation than methods. 11,15,26,30 In this table, the efficient weighted LS algorithm 30 using Toeplitz-plus-Hankel matrix to the design of IIR all-pass filters is also included for FIGURE 4 The design procedure of IIR all-pass-based QMF banks using neural networks comparison. 11,15 The designed magnitude error response of QMF banks surpasses those of methods 11,15 which can be seen from Figure 5D.…”

“…11,15 Figure 5B, C depicts that FIGURE 3 The design of IIR all-pass-based QMF banks using Hopfield neural network (i = 1, 2) the proposed neural-based approach has smaller phase error and group delay error responses than methods. 11,15 Because the design accuracy is indistinguishable as compared with the methods of Jou et al 26 and Kidambi,30 the resulting plots of methods 26,30 are ignored in Figure 5. Table 2 lists the IIR all-pass filter coefficients designed using various techniques.…”