Chapter 3 Pulse Code Modulation Pulse Code Modulation

  • Slides: 20
Download presentation
Chapter 3: Pulse Code Modulation Ø Ø Ø Pulse Code Modulation Quantizing Encoding Analogue

Chapter 3: Pulse Code Modulation Ø Ø Ø Pulse Code Modulation Quantizing Encoding Analogue to Digital Conversion Bandwidth of PCM Signals Huseyin Bilgekul Eeng 360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 360 1

PULSE CODE MODULATION (PCM) Ø DEFINITION: Pulse code modulation (PCM) is essentially analog-to-digital conversion

PULSE CODE MODULATION (PCM) Ø DEFINITION: Pulse code modulation (PCM) is essentially analog-to-digital conversion of a special type where the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream. Ø The advantages of PCM are: • Relatively inexpensive digital circuitry may be used, • PCM signals derived from all types of analog sources may be merged with data signals and transmitted over a common high-speed digital communication system, • In long-distance digital telephone systems requiring repeaters, a clean PCM waveform can be regenerated at the output of each repeater, where the input consists of a noisy PCM waveform, • The noise performance of a digital system can be superior to that of an analog system, • The probability of error for the system output can be reduced even further by the use of appropriate coding techniques. Eeng 360 2

Sampling, Quantizing, and Encoding Ø The PCM signal is generated by carrying out three

Sampling, Quantizing, and Encoding Ø The PCM signal is generated by carrying out three basic operations: 1. Sampling 2. Quantizing 3. Encoding 1. 2. Sampling operation generates a flat-top PAM signal. Quantizing operation approximates the analog values by using a finite number of levels. This operation is considered in 3 steps a) Uniform Quantizer b) Quantization Error c) Quantized PAM signal output 3. PCM signal is obtained from the quantized PAM signal by encoding each quantized sample value into a digital word. Eeng 360 3

Analog to Digital Conversion Ø The Analog-to-digital Converter (ADC) performs three functions: – Sampling

Analog to Digital Conversion Ø The Analog-to-digital Converter (ADC) performs three functions: – Sampling Analog Input Signal • Makes the signal discrete in time. • If the analog input has a bandwidth of W Hz, then the minimum sample frequency such that the signal can be reconstructed without distortion is 2 W or more. Sample ADC – Quantization Quantize Encode Digital Output Signal 111 001 010 011 111 110 101 100 011 010 001 000 • Makes the signal discrete in amplitude. • Round off to one of q discrete levels. – Encode • Maps the quantized values to digital words that are bits long. Ø If the (Nyquist) Sampling Theorem is satisfied, then only quantization introduces distortion to the system. Eeng 360 4

Quantization Ø The output of a sampler is still continuous in amplitude. – Each

Quantization Ø The output of a sampler is still continuous in amplitude. – Each sample can take on any value e. g. 3. 752, 0. 001, etc. – The number of possible values is infinite. Ø To transmit as a digital signal we must restrict the number of possible values. Ø Quantization is the process of “rounding off” a sample according to some rule. – E. g. suppose we must round to the nearest tenth, then: 3. 752 --> 3. 8 0. 001 --> 0 Eeng 360 5

Illustration of the Quantization Error Eeng 360 6

Illustration of the Quantization Error Eeng 360 6

PCM TV transmission: (a) 5 -bit resolution; (b) 8 -bit resolution. Eeng 360 7

PCM TV transmission: (a) 5 -bit resolution; (b) 8 -bit resolution. Eeng 360 7

Uniform Quantization Dynamic Range: (-8, 8) Output sample XQ 7 5 3 1 -8

Uniform Quantization Dynamic Range: (-8, 8) Output sample XQ 7 5 3 1 -8 -6 -4 -2 -1 2 4 6 8 Input sample X -3 -5 -7 Quantization Characteristic Example: Uniform =3 bit quantizer q=8 and XQ = { 1, 3, 5, 7} • Most ADC’s use uniform quantizers. • The quantization levels of a uniform quantizer are equally spaced apart. • Uniform quantizers are optimal when the input distribution is uniform. When all values within the Dynamic Range of the quantizer are equally likely. Eeng 360 8

Types of Quantization There are two types of Quantization - Uniform Quantization and Non-uniform

Types of Quantization There are two types of Quantization - Uniform Quantization and Non-uniform Quantization. The type of quantization in which the quantization levels are uniformly spaced is termed as a Uniform Quantization. The type of quantization in which the quantization levels are unequal and mostly the relation between them is logarithmic, is termed as a Non-uniform Quantization. There are two types of uniform quantization. They are Mid-Rise type and Mid. Tread type. The following figures represent the two types of uniform quantization. Eeng 360 9

 • The Mid-Rise type is so called because the origin lies in the

• The Mid-Rise type is so called because the origin lies in the middle of a raising part of the stair-case like graph. The quantization levels in this type are even in number. • The Mid-tread type is so called because the origin lies in the middle of a tread of the stair-case like graph. The quantization levels in this type are odd in number. • Both the mid-rise and mid-tread type of uniform quantizers are symmetric about the origin. Eeng 360 10

Quantization Example Analogue signal Sampling TIMING Quantization levels. Quantized to 5 -levels Quantization levels

Quantization Example Analogue signal Sampling TIMING Quantization levels. Quantized to 5 -levels Quantization levels Quantized 10 -levels Eeng 360 11

PCM encoding example Levels are encoded using this table Table: Quantization levels with belonging

PCM encoding example Levels are encoded using this table Table: Quantization levels with belonging code words M=8 Chart 1. Quantization and digitalization of a signal. Signal is quantized in 11 time points & 8 quantization segments. Chart 2. Process of restoring a signal. PCM encoded signal in binary form: 101 110 001 010 100 111 100 011 010 101 Total of 33 bits were used to encode a signal Eeng 360 12

Encoding • The output of the quantizer is one of M possible signal levels.

Encoding • The output of the quantizer is one of M possible signal levels. – If we want to use a binary transmission system, then we need to map each quantized sample into an n bit binary word. • Encoding is the process of representing each quantized sample by a bit code word. – The mapping is one-to-one so there is no distortion introduced by encoding. – Some mappings are better than others. • A Gray code gives the best end-to-end performance. • The disadvantage of Gray codes is that they will give poor performance when the sign bit (MSB) is received in error. Eeng 360 13

Gray Codes • With gray codes adjacent samples differ only in one bit position.

Gray Codes • With gray codes adjacent samples differ only in one bit position. • Example (3 bit quantization): XQ +7 +5 +3 +1 -1 -3 -5 -7 Natural coding 111 110 101 100 011 010 001 000 Gray Coding 110 111 100 001 010 • With this gray code, a single bit error will result in an amplitude error of only 2. – Unless the MSB is in error. Eeng 360 14

Waveforms in a PCM system for M=8 (a) Quantizer Input output characteristics (b) Analog

Waveforms in a PCM system for M=8 (a) Quantizer Input output characteristics (b) Analog Signal, PAM Signal, Quantized PAM Signal (c) Error Signal (d) PCM Signal Eeng 360 15

PCM Transmission System Eeng 360 16

PCM Transmission System Eeng 360 16

To implement the analog-to-digital converter (ADC) encoding operation 1) Counting or ramp encoder 2)

To implement the analog-to-digital converter (ADC) encoding operation 1) Counting or ramp encoder 2) Serial or successive approximation encoder 3) Parallel or flash encodes In the counting encoder, at the same time the sample is taken, a ramp generator is energized (started) and a binary counter is started. The output of the Ramp generator is continuously compared with the sample value When the ramp value equals the sample value the binary value of the counter is read. This count is Taken as the PCM word. Speed of this type ADC is limited with the speed of The counter. Eeng 360 17

Practical PCM Circuits 1. 2. 3. • • The counting or ramp, ( Maxim

Practical PCM Circuits 1. 2. 3. • • The counting or ramp, ( Maxim ICL 7126 ADC) Serial or successive approximation, (AD 570) Parallel or flash encoders. ( CA 3318) The objective of these circuits is to generate the PCM word. Parallel digital output obtained (from one of the above techniques) needs to be serialized before sending over a 2 -wire channel This is accomplished by parallel-to-serial converters [Serial Input-Output (SIO) chip] UART, USRT and USART are examples for SIO’s Eeng 360 18

Bandwidth of PCM Signals • Eeng 360 19

Bandwidth of PCM Signals • Eeng 360 19

Eeng 360 20

Eeng 360 20