diff PCM - Chapter 6 Quantization To convert an analog...

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6-1 Chapter 6. Quantization To convert an analog signal to a digital signal, the following three procedures are required. First, the signal is passed through a lowpass filter to prevent aliasing. Second, the signal is sampled by a sample-and-hold circuit. Finally, the samples are quantized by an analog to digital converter (ADC) in order to be represented in digital form as shown in Figure 6.1. x ( t ) Anti-aliasing x ( n ) $ () x n Filter Sample-and-hold A/D Converter (Analog Signal) (LPF) Circuit (Discrete-time (Digital Signal) S i g n a l ) Figure 6.1. Typical analog to digital conversion process There are many different kinds of quantization techniques available. Quantization methods such as the linear quantization, the nonlinear quantization, the delta modulation, and the sigma-delta modulation are described in this chapter. Also efficient quantization methods such as the adaptive quantization and the differential quantization are explained. The Adaptive Differential Pulse Code Modulation (ADPCM) is also described. 6.1 Linear Quantization In linear or uniform quantization , the quantization step size is fixed. The constant quantization step size is used no matter what the instantaneous signal amplitude is. Linear quantization with 2 m quantization levels is shown in Figure 6.2 where is the quantization step size and m is the number of bits in a quantization word. Sample value in volts[V] (2 m 1) /2 (Positive Peak Value = 2 m /2: loudest) (2 m 3) /2 3 /2 /2 (softest) −∆ /2 (softest) 3 /2 (2 m 3) /2 (2 m 1) /2 (Negative Peak Value = 2 m /2: loudest) Figure 6.2. Constant quantization step size is used for linear quantization. ( m is the number of bits used for quantization)
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6-2 For example, if the peak to peak value of a signal is 4 [V] and m = 3, then the signal may be quantized according to the rule shown in Figure 6.3. Digital value after quantization (1.75) 111 (1.25) 110 (0.75) 101 (0.25) 100 Sample value before 2 1.5 1 0.5 0 0.5 1 1.5 2 quantization [V] 011 ( 0.25) 010 ( 0.75) 001 ( 1.25) 000 ( 1.75) Figure 6.3. Three-bit linear quantization example. (sign-magnitude binary representation is used) In this case = 0.5 [V]. A value between 0 and 0.5 is approximated (or quantized) by the quantization level /2 (0.25) and encoded by 100. A value between 0.5 and 1.0 is quantized by the quantization level 3 /2 (0.75) and encoded by 101. Likewise, a value between 2 and 1.5 is quantized by the level 7 /2 ( 1.75) and encoded by 000 and so on. The process of sampling, quantization and encoding is referred to as the pulse code modulation (PCM). Keeping a step size fixed is especially essential for high-fidelity digital audio. One notable example is the compact disc (CD) format. The CD format uses 16 bit linear quantization so that the range between the negative peak and the positive peak is divided by 2 16 (65,536) uniform quantization levels.
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This note was uploaded on 02/05/2012 for the course EE EE308 taught by Professor B.k.dey during the Spring '09 term at IIT Bombay.

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diff PCM - Chapter 6 Quantization To convert an analog...

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