A simple design of M-channel FIR wavelet-like filter bank

In this paper, we propose a simple method for designing M-channel FIR wavelet-like filter banks. Unlike the conventional design of wavelet filter banks, our approach is based on near-perfect-reconstruction (NPR) filter banks, justifying the name "wavelet-like." The major contribution of this paper lies in the technique to impose regularity constraints individually into each filter of the NPR filter bank, yielding more free parameters to design wavelet-like filter banks. Moreover, our method involves no optimization procedure by imposing regularity constraints. The designed 1-regular wavelet-like filter bank possesses good properties as the original NPR filter bank. The 2-regular wavelet-like filter bank can also be obtained preserving the NPR property. Examples are given to numerically illustrate the proposed technique.