Lecture 10: Quantizing & PCM 1nd semester 1439-2017 By: Adal ALashban

Introduction - A digital signal is superior to an analog signal because it is more robust to noise and can easily be recovered, corrected and amplified. - For this reason, the tendency today is to change an analog signal to digital data. - Changing analog signal to digital signal: Sampling  Quantizing

Quantization - In order to process the sampled signal digitally, the sample values have to be quantized to a finite number of levels, and each value can then be represented by a string of bits. - To quantize a sample value is to round it to the nearest point among a finite set of permissible values. - Therefore, a distortion will inevitably occur. This is called quantization noise (or error).

Quantization

Continuous wave (CW) modulation AM Angle modulation FM PM Pulse Modulation Analog Pulse Modulation PAM PPM PDM Digital Pulse Modulation DM PCM

Pulse-code Modulation (PCM) - Pulse-code Modulation (PCM), like PAM, is a digital communication technique that sends samples of the analog signal taken at a sufficiently high rate. - PCM differs than PAM in that it quantizes the samples by constraining them to only take a limited number of values, and then converts each value into a binary string of bits that are transmitted on the communication line.

Pulse-code Modulation (PCM) - PCM consists of three steps to digitize an analog signal: 1. Sampling 2. Quantization 3. Binary encoding - Before we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate. - Filtering should ensure that we do not distort the signal, i.e. remove high frequency components that affect the signal shape.

Components of PCM Encoder

Sampling - Analog signal is sampled every Ts secs. - Ts is referred to as the sampling interval or period. - fs = 1/Ts is called the sampling rate or sampling frequency. - The process is referred to as pulse amplitude modulation PAM and the outcome is a signal with analog (non integer) values.

Note - According to the Nyquist theorem, the sampling rate must be at least 2 times the highest frequency contained in the signal.

Recovery of a sampled sine wave for different sampling rates

Quantization  = (max - min)/L - Sampling results in a series of pulses of varying amplitude values ranging between two limits: a min and a max. - The amplitude values are infinite between the two limits. - We need to map the infinite amplitude values onto a finite set of known values. - This is achieved by dividing the distance between min and max into L zones, each of height height  = (max - min)/L

Quantization Levels - The midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values) n

- Each sample falling in a zone is then approximated to the value of the midpoint. approximating the value of the sample amplitude to the quantized values. 1 2 3

Assigning Codes to Zones - Each zone is then assigned a binary code. - The number of bits required to encode the zones, or the number of bits per sample as it is commonly referred to, is obtained as follows: nb = log2 L - Given our example, nb = 2 - The 4 zone (or level) codes are therefore: 00, 01, 10, 11

Assigning Codes to Zones Each zone is assigned a binary code 1 2 3 00 01 10 11

Assigning Codes to Zones Use one of the line code scheme to get the digital signal

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