Orthonormal FBs With Rational Sampling Factors and Oversampled DFT-Modulated FBs: A Connection and Filter Design

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Methods widely used to design filters for uniformly sampled filter banks (FBs) are not applicable for FBs with rational sampling factors and oversampled discrete Fourier transform (DFT)-modulated FBs. In this paper, we show that the filter design problem (with regularity factors/vanishing moments) for these two types of FBs is the same. Following this, we propose two finite-impulse-response (FIR) filter design methods for these FBs. The first method describes a parameterization of FBs with a single regularity factor/vanishing moment. The second method, which can be used to design FBs with an arbitrary number of regularity factors/vanishing moments, uses results from frame theory. We also describe how to modify this method so as to obtain linear phase filters. Finally, we discuss and provide a motivation for iterated DFT-modulated FBs. </para>