Audio Signal Processing and Coding

2.5 DISCRETE-TIME SIGNAL PROCESSING

Audio coding algorithms operate on a quantized discrete-time signal. Prior to compression, most algorithms require that the audio signal is acquired with high-fidelity characteristics. In typical standardized algorithms, audio is assumed to be bandlimited at 20 kHz, sampled at 44.1 kHz, and quantized at 16 bits per sample. In the following discussion, we will treat audio as a sequence, i.e., as a stream of numbers denoted . Initially, we will review the discrete-time signal processing concepts without considering further aliasing and quantization effects. Quantization effects will be discussed later during the description of specific coding algorithms.

2.5.1 Transforms for Discrete-Time Signals

Discrete-time signals are described in the transform domain using the z-transform and the discrete-time Fourier transform (DTFT). These two transformations have similar roles as the Laplace transform and the CFT for analog signals, respectively. The z-transform is defined as

where z is a complex variable. Note that if the z-transform is evaluated on the unit circle, i.e., for

then the z-transform becomes the discrete-time Fourier transform (DTFT). The DTFT ...