Communication Theory II

Size: px

Start display at page:

Download "Communication Theory II"

Adela Hodges
6 years ago
Views:

1 Communication Theory II Lecture 18: Pulse Code Modulation Ahmed Elnakib, PhD Assistant Professor, Mansoura University, Egypt April 19 th,

2 Lecture Outlines opulse Code Modulation (PCM) Sampling and Pulse Amplitude Modulation Quantization Uniform quantization vs non uniform quantization Compressor and expander (compander) Encoding Bandwidth of PCM 2

3 Pulse Code Modulation (PCM) o Method of converting an analog into digital signal (A/D conversion) o Composed of three components: sampling, quantizing, and encoding 3

4 Block Diagram of PCM System 4

5 Sampling Methods othere are 3 sampling methods: Ideal - an impulse at each sampling instant Natural - a pulse of short width with varying amplitude Flattop - sample and hold, like natural but with single amplitude value 5

6 Pulse Amplitude Modulation (PAM) o PAM is a linear modulation process where the amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal. Flat-top samples o In contrast to ideal sampling, it involve two operation: Instantaneous sampling of the message signal m(t) every T s seconds, where the sampling rate f s = 1/T s is chosen in accordance with the sampling theorem Lengthening the duration of each sample so obtained to some constant value T 6

Quantization L=8 m p = 20 17.5 12.5 7.5 2.5-2.5-7.5-12.5-17.5 sampled signal 7.5 16.2 19.7 11-5.5-11.3-9.4-6 Quantized signal -7.5 7.5 17.5 17.5 12.5-7.5-6.1-7.5-7.5 Quantization Error 1.4 0-1.3 2.

7 Quantization L=8 m p = sampled signal Quantized signal Quantization Error v=2m p /L=2.5 o Rounding the analog signal value to one of the closest permissible numbers (quantization levels) o Number of levels: L=8 levels L-ary digital signal o Interval width: v= (max - min)/l o If m(t) lies between m p,-m p v=2m p /L Amplitude of m(t) beyond ± mmmm is chopped o Each sample falling in a zone (subinterval) is then approximated to the value of the midpoint o Maximum quantization error ± v/2

8 Quantization osampling results in a series of pulses of varying amplitude values ranging between two limits: a min and a max. othe amplitude values are infinite between the two limits. owe need to map the infinite amplitude values onto a finite set of known values. othis is achieved by dividing the distance between min and max into L zones, each of height v. v= (max - min)/l

9 Quantization Levels othe midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values) oeach sample falling in a zone is then approximated to the value of the midpoint.

10 Quantization Zones oassume we have a voltage signal with amplitutes V min =-20V and V max =+20V. owe want to use L=8 quantization levels. ozone width = ( )/8 = 5 othe 8 zones are: -20 to -15, -15 to -10, -10 to -5, -5 to 0, 0 to +5, +5 to +10, +10 to +15, +15 to +20 othe midpoints are: -17.5, -12.5, -7.5, -2.5, 2.5, 7.5, 12.5, 17.5

11 Types of Uniform Quantization To have a zero output level Two types of uniform quantization: (a) midtread and (b) midrise Both are uniform quantization and symmetric about the origin 11

12 Assigning Codes to Zones (subintervals) oeach zone is then assigned a binary code. othe 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: n = log 2 L ogiven our example, n= 3 othe 8 zone (or level) codes are therefore: 000, 001, 010, 011, 100, 101, 110, and 111 oassigning codes to zones: 000 will refer to zone -20 to to zone -15 to -10, etc.

13 Quantization noise Illustration of the quantization process. 13

14 Quantization noise 14

15 Random Uniformly distributed Quantization Noise 15

16 Signal to Noise Ratio 16

17 Problems of Uniform Quantization: S/N depends on the message signal power Solution 1: using a non uniform quantizer with non uniform levels Solution 2: using a compressor with logarithmic characteristics followed by a uniform quantizer 17

18 Non-uniform Quantization (a) Nonuniform quantization of the message signal in the transmitter (b) Uniform quantization of the original message signal in the receiver 18

Example 1: Sampling of telephone voice signal o An audio signal bandwidth is about 15 khz Subjective tests show that he signal articulation is not affected if all the components above 3.

19 Example 1: Sampling of telephone voice signal o An audio signal bandwidth is about 15 khz Subjective tests show that he signal articulation is not affected if all the components above 3.4 khz are suppressed An anti-aliasing filter suppress all the components above 3.4 khz before sampling o Typical sampling rate used is f s =8kHz (higher than the Nyquist rate to avoid unrealizable filters for signal reconstruction) Cut-off frequency 3.4 khz Transition band 6.8 to 8kHz o Each sample is finally quantized into 256 levels (L=256=2 8 ), which require 8 bits to encode each sample o The telephone signal require 8x8000=64k pulses per second 19

20 Example 2: Sampling of voice signal on a Compact Disk (CD) o An audio signal bandwidth is about 15 khz An anti-aliasing filter suppress all the components above 15 khz before sampling o Typical sampling rate used is f s =44.1kHz (higher than the Nyquist rate to avoid unrealizable filters for signal reconstruction) o Each sample is finally quantized into 65,536 levels (L=2 16 ), which require 16 bits to encode each sample o The audio signal on a typical CD require 16x44.1k=705.6k pulses per second 20

21 Questions 21

Communication Theory II

Communication Theory II Lecture 17: Conversion of Analog Waveforms into Coded Pulses Ahmed Elnakib, PhD Assistant Professor, Mansoura University, Egypt April 16 th, 2015 1 opulse Modulation Analog Pulse