Design of two‐channel perfect reconstruction QMF

This paper proposes a design method for the FIR two‐channel perfect quadrature mirror filter (QMF) with the linear phase. The two‐channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics. This paper presents the design for the two‐channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude characteristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations. The construction of the two‐channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two‐dimensional (2‐D) perfect QMF is designed by applying the McClellan transformation to the obtained 1‐D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived.