The design of M-channel linear phase wavelet-like filter banks

This paper investigates M-channel linear-phase (LP) wavelet-like filter banks. The term "wavelet-like" is justified because the filter bank is of near-perfect-reconstruction (NPR). We firstly derive some conditions for designing M-channel LP NPR filter banks and then propose a design method of wavelet-like filter banks. The proposed wavelet-like filter bank is obtained by imposing regularity constraints on the LP NPR filter bank. By using some simple algebraic transformations, we convert the original filter into the wavelet-like filter without nonlinear optimization. With this method, we not only preserve the desired LP property, but also obtain good NPR property as the original NPR filter bank, such as high stopband attenuation. Finally, examples show that LP wavelet-like filter banks with even and odd numbers of channels are capable of achieving different degrees of regularity.