Construction of 4-band linear-phase orthogonal perfect-reconstruction filter banks using iterative eigenfilter method

This paper presents an eigenfilter based method for the design of 4-band perfect reconstruction (PR) filter banks. All the filters of the filter bank exhibit linear phase and orthogonality property. The eigenfilter method has been used so far to impose linear constraints on the filter, however, in this paper, we discuss how to impose nonlinear constraints on the filter using the eigenfilter method. The analysis lowpass filter impulse response is obtained using an iterative approach in the eigenfilter method to minimize the error as given by the alias cancellation equations in the PR filter bank. Once the analysis lowpass filter impulse response h₀[n] is obtained, the other filters are obtained using shuffling matrices. We present two design examples of a 4-channel perfect reconstruction filter bank. We also report a minor modification in the eigenfilter method for imposing non-homogeneous linear constraints on the filter.