From Mixed Signal VLSI Wireless Design: Circuits and Systems
Quantization is the process of approximating a continuous analog signal to discrete levels, i.e. quantization is a many-to-one mapping. If these levels are uniformly spaced, the quantizer is a uniform quantizer. However, if these levels are unevenly spaced, the quantizer is a non-uniform quantizer.
Assume that the separation between any two consecutive quantization levels is the step-size ?. In a uniform quantizer ? is constant. Assume that, Q is the total number of quantization levels. In an analog-to-digital converter each quantization level is mapped into a binary power code. Hence, Q is a power of 2:
Where n is the number of bits at the output of the analog-to-digital converter. Figures 7.11 and 7.12 show two examples for the transfer function of the quantizer. Each transfer function consists of Q treads, each separated by ? and having a width ?.
Figure 7.11: Staircase transfer function of a mid-tread quantizer.
Figure 7.12: Staircase transfer function of a mid-rise quantizer.
The quantizer of Figure 7.11 is known as a mid-tread quantizer, this is because the origin is at the middle of a tread. The transfer function for this quantizer can be expressed by the following expression:
Notice that, for the mid-tread quantizer, the quantization levels are symetric around the zero. However, there is no zero quantization level, i.e. the quantized signal is either positive or negative.
The quantizer of Figure 7.12 is known as a mid-rise quantizer, this...
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