Design of even and ODD components of lowpass paraunitary 2-channel filters

This paper addresses the problem of obtaining real FIR paraunitary filters. In this work, we present an algorithm which designs the even and odd components of 2-channel FIR orthogonal lowpass filters. We show that any vector of length L may contain the even coefficients of an 2L-tap orthogonal filter (up to a factor); moreover, we explain how to compute the odd part of such filter. In the lowpass case, we give a sufficient condition on the vector in order to design lowpass paraunitary filters. To illustrate our method, some examples of lowpass 4-taps filters are designed.