Dual Channel Speech Enhancement Based on Fractional Fourier Transform

Abstract

This chapter provides a detailed implementation of speech enhancement algorithm using fractional Fourier transform technique. Dual channel adaptive noise cancellation setup has been considered for the present study. Two adaptive algorithms, viz. LMS and NLMS algorithms, are implemented in FrFT domain. FrFT-based adaptive filters overcome the difficulties of adaptation in time-varying signal environment by transforming the signals into fractional Fourier domain, where signals vary slowly. The advantage of using the fractional Fourier domain is that the non-bandlimited signal in Fourier domain may be bandlimited in the fractional Fourier domain for a certain value of angle. In this chapter, special attention has been given to the concepts of continuous fractional Fourier transform (CFrFT) technique and its digital implementation. As preliminaries, the basics of ANC and adaptive filters are described in Sect. 3.1. Adaptive filters are described in Sect. 3.2. Adaptive filters in FrFT domain and the application of FrFT-based adaptive filters to speech enhancement are discussed in Sect. 3.3. The mathematical formulae and the background concepts of objective measures used for the evaluation of algorithms have also been presented. Results, analysis, and the conclusions of this chapter are given in Sects. 3.4 and 3.5, respectively.