Prototype filter design for arbitrary delay exponentially-modulated filter bank

In this paper we formulate the prototype filter design problem for arbitrary delay exponentially-modulated filter banks. Further on, we set a constraint for the two lowpass analysis subfilters to capture the constant component of the complex-valued input signal. This is the polyphase normalization property for odd-stacked exponential modulation. The perfect reconstruction conditions are given in a programming language friendly form. A generalization of the design problem is presented to provide arbitrary delay and arbitrary length prototypes for modulated filter banks.