DAFX: Digital Audio Effects, Second Edition

7.1 Introduction

This chapter describes the use of time-frequency representations of signals in order to produce transformations of sounds. A very interesting (and intuitive) way of modifying a sound is to make a two-dimensional representation of it, modify this representation in some way and reconstruct a new signal from this representation (see Figure 7.1). Consequently a digital audio effect based on time-frequency representations requires three steps: an analysis (sound to representation), a transformation (of the representation) and a resynthesis (getting back to a sound).

Figure 7.1 Digital audio effects based on analysis, transformation and synthesis (resynthesis).

The direct scheme of spectral analysis, transformation and resynthesis will be discussed in Section 7.2. We will explore the modification of the magnitude |X(k)| and phase φ(k) of these representations before resynthesis. The analysis/synthesis scheme is termed the phase vocoder (see Figure 7.2). The input signal x(n) is multiplied by a sliding window of finite length N, which yields successive windowed signal segments. These are transformed to the spectral domain by FFTs. In this way a time-varying spectrum with k = 0, 1, …, N − 1 is computed for each windowed segment. The short-time spectra can be modified or ...