Digital Audio Signal Processing, 3rd Edition

Chapter 3Sampling Rate Conversion

U. Zölzer

Several different sampling rates are established for digital audio applications. For broadcasting, professional, and consumer audio, sampling rates of 32, 48, and 44.1 kHz are used, respectively. Moreover, other sampling rates are derived from different frame rates for film and video. In connecting systems with different uncoupled sampling rates, there is a need for sampling rate conversion. In this chapter, synchronous sampling rate conversion with rational factor for coupled clock rates and asynchronous sampling rate conversion will be discussed where the different sampling rates are not synchronized with each other.

3.1 Basics

Sampling rate conversion consists of upsampling and downsampling and anti‐imaging and antialiasing filtering [Cro83, Vai93, Fli00, Opp99]. The discrete‐time Fourier transform of the sampled signal with sampling frequency () is given by

(3.1)

with the Fourier transform of the continuous‐time signal . For ideal ...