Audio Signal Processing and Coding

3.3 SCALAR QUANTIZATION

In this section, we describe the various scalar quantization schemes. In particular, we review uniform and nonuniform quantization, and then we present differential PCM coding methods and their adaptive versions.

3.3.1 Uniform Quantization

Uniform PCM is a memoryless process that quantizes amplitudes by rounding off each sample to one of a set of discrete values (Figure 3.3). The difference between adjacent quantization levels, i.e., the step size, Δ, is constant in non-adaptive uniform PCM. The number of quantization levels, Q, in uniform PCM binary representations is , where R_b denotes the number of bits. The performance of uniform PCM can be described in terms of the signal-to-noise ratio (SNR). Consider that the signal, s, is to be quantized and its values lie in the interval

Figure 3.3. (a) Uniform PCM and (b) uniform quantization of a triangular waveform. From the figure, R_b = 3 bits; Q = 8 uniform quantizer levels.

A uniform step size can then be determined by

Let us assume that the quantization noise, e_q, has a uniform PDF, i.e.,

From (3.9), (3.10) ...