From Mixed Signal VLSI Wireless Design: Circuits and Systems

7.5 QUANTIZATION

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:

(7.23)

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:

(7.24)

Where, .

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...


Products & Services
Stairs and Stairways
Stairs and stairways include all types of complete, pre-fabricated stair systems and staircases.
Digital-to-Analog Converters
Digital-to-analog converters (DAC) transform a digital number into a corresponding analog voltage or current.
Stair Treads and Nosings
Stair treads and nosings are stair and staircase components that provide wear resistance, corrosion resistance, structural, and anti-slip functionality.
Data Acquisition Computer Boards
Data acquisition computer boards are self-contained printed circuit boards that typically plug into the backplane, motherboard, or otherwise interface directly with the computer bus.
Digital-to-Analog Converter (DAC) Chips
Digital-to-analog converter (DAC) chips convert digital signals that represent binary numbers into proportional analog voltages.

Topics of Interest

7.6 TYPES OF ANALOG-TO-DIGITAL CONVERTERS Analog-to-digital converters are classified into one-step architectures, such as: flash, folding and interpolative topologies, and multi-step architectures,...

AN643 Adaptive Differential Pulse Code Modulation ® Using PIC Microcontrollers 3.00. The ITU (formerly CCITT) G.721 ADPCM algo- Author: Rodger Richey rithm is well known and has been implemented...

Objectives: This chapter studies speech quantization and compression techniques such as signal companding, differential pulse code modulation, and adaptive differential pulse code modulation. The...

7.7 SIGMA-DELTA ANALOG-TO-DIGITAL CONVERTERS Sigma-Delta analog-to-digital converters are commonly used when high resolution is required, this is because of the sigma-delta modulator s ability to...

This chapter is devoted to engineering applications using appropriate Simulink blocks to illustrate the application of the blocks in the libraries which we described in Chapters 2 through 18. Most of...

Product Announcements
High Performance Alloys, Inc.
Henkel Corporation - Industrial