Pitch Shifting by H∞-Optimal Variable Fractional Delay Filters

Abstract

AbstractFractional delay filters are those that are designed to delay the input samples by a fractional amount of the sampling period. Since the delay is fractional, the intersample behavior of original analog signals becomes crucial. For this, we propose an optimal design via sampled-data H∞ control theory. By this theory, our design problem is equivalently reduced to a discrete-time H∞ optimization, and, an analytical solution is obtained under an assumption on the original analog signals. Using this analytical solution, we propose a sampling rate conversion with arbitrary conversion rate. This conversion is much faster than conventional methods using an upsampler, a digital filter, and a downsampler. We also show an application of the proposed sampling rate conversion to pitch shifting of guitar sounds. A design example is shown to illustrate the advantage of the proposed method.