Chapter 8 - PSAU · Prepared by Prof.V.K.Jain 15 Pulse Code Modulation (PCM) zIn PCM, the available range of signal is divided into N levels and each assigned a binary number. zEach

Prepared by Prof.V.K.Jain 1

Chapter 8

Digital Transmission


Lecture Outcome

On completing of this lecture, you should be able to:Compare analog and digital communication techniquesCalculate the information capacity of a channelDescribe the common types of analog pulse modulationDescribe PCM and dynamic rangeDescribe signal companding


Introduction

Digital communication is the transmittal of digital pulses between two or more points.Original source can be in digital or in analog forms.Analog signal needs to be digitized prior to transmission.Digital communication also need a channel for transmission as required by the analog communication.


Advantages of Digital Transmission

Better immunity against noise than analog.Better suited than analog for processing, storage, and combination using multiplexing. Simpler to measure and evaluate than analog.Transmission errors can be detected and corrected more easily and correctly than is possible with analog.


Digital systems advantages


Digital systems advantages


Disadvantages of Digital Transmission

Transmission of digitally encoded analog signals requires significantly more bandwidth than analog transmission.Analog signal must be first converted to digital pulses prior to transmission and converted back to analog at receiver.Digital transmission requires precise time synchronization between the clocks in transmitter and receiver.


Sampling

To transmit analog signal by digital means, it is first necessary to sample it.In 1928, Harry Nyquist proved, signal can be reconstructed from periodic samples as long as sampling rate is at least twice the highest frequency of the signal.

In telephony, sampling frequency is 8 kHz for maximum audio frequency of 3.4 kHz.In CD system, sampling frequency is 44.1 kHz for maximum audio frequency of 20 kHz.


Sampling


Sampling frequency or sampling rate, fs ≥ 2fmSampling interval, Ts ≤ 1/fsNyquist sampling rate or Nyquist rate = 2fmNyquist interval = 1/2fmSpeech signal, fm = 3.4 kHz

Sampling rate, fs ≥ 6.8 kHz

≥ 6800 samples/s

Practical sampling rate, fs = 8000 samples/s

Sampling interval, Ts = 1/8000

= 125 μs


The highest frequency components present in a signal, fm is determined from its frequency spectrum.

cos (100πt) ; fm= 50 Hz

cos2 (100πt) ; fm= 100 Hz

cos 3(100πt) ; fm= 150 Hz

cos (100πt)cos(60πt) ; fm= 80 Hz

For no distortion, fs ≥ 2fm

)(1)(0

sns

s fnfGT

fG ∑∞

=

−=


Time Division Multiplexing (TDM)US T1 1.544 Mb/s 24 Voice Signals

T2 6.312 96T3 44.736 672T4 274.176 4032

Europe E1 2.048 30E2 8.448 120E3 34.368 480E4 139.264 1920E5 564.992 7680


Pulse modulation

Pulse modulation consists of sampling, converting samples to pulses, and transmission over a physical medium.Four major pulse modulation techniques

Pulse Width Modulation (PWM)Pulse Position Modulation (PPM)Pulse Amplitude Modulation (PAM)Pulse Code Modulation (PCM)


Pulse Modulation


Pulse Code Modulation (PCM)

In PCM, the available range of signal is divided into N levels and each assigned a binary number.Each sample is represented by the closest level to its amplitude.In linear PCM, levels are separated by equal voltage gradations.In nonlinear PCM, levels are separated by unequal voltage gradations.Number of levels depends on number of bits to express each sample (level). 2nN =


Quantization and Binary Coding

Three-bit PCM Code

110 001 111110 001 111



Calculate number of levels if number of bits per sample is:

8 ( as in telephony)16 ( as in CD audio system)

8

16

22 256 ( )2 65,536 ( )

nNin telephony

in CD audio systems

=

= =

= =


Pulse Code Modulation (PCM)



Since number of levels is finite, quantizing process produces errors called quantization error (Qe) or quantization noise (Qn).The maximum magnitude for Qe is equal to one-half a quantum (±0.5V for code in table)Quantizing noise can be reduced by increasing number of levels or number or bits per sample.Increasing number of bits per sample increases data rate, which is given by

(bits/s)sD f n=


Quantization and Binary CodingDynamic Range (DR)

Quantum is the difference between adjacent levels.Magnitude of quantum is called resolution.

Resolution of PCM code shown in table is 1 V.

Dynamic range (DR) is the ratio of largest possible magnitude to the smallest possible magnitude (other than zero) that can be decoded by D/A at receiver.

max max

min

( ) 20log( )

V VDRV resolution

DR dB DR

= =

=



For linear PCM, the relationship between DR (dB) and number of bits in PCM code is

Signal to noise ratio (SNR) for PCM system is given as

( )

max

min

20 log

20log 2 1

6

n

VDRV

n

⎛ ⎞= ⎜ ⎟

⎝ ⎠

= −

≅

[ ]dBnSNR 02.676.1 +=



Find the maximum dynamic range and SNR of a linear PCM using 16-bits quantizing.

Calculate the data rate needed to transmit audio with sampling rate 40 kHz and 14 bits per sample.

66 16 96

DR n dBdB

≅≅ × =

3 340 10 14 560 10 560 / sD f n

kb s

= ×

= × × = × =

( )( )1.76 6.02

1.76 96.32 98.08

SNR n dB

dB dB

= +

= + =


Signal-to-Quantization Noise Ratio (SQR)

With linear PCM codes, all quantization intervals have equal magnitudes.Signal power-to-quantizing noise power ratio is determined as:

v = rms signal voltage (volts)q = quantization interval (volts)

( )12/log10)( 2

2

qvdBSQR =


Uniform and Nonuniform Quantization


Companding

Companding is the process of compression at transmitter and then expanding at receiver.With companded systems, higher amplitude signals are compressed prior to transmission and then expanded after detection.Compressor reduces quantizing error for small signals.Different signal distributions require different companding characteristics.


Companding

North American telephone system uses characteristic know as μ-law as equation for compressor:

Vin(max) = maximum uncompressed analog input (volts)vin = amplitude of input signal at particular time (volts)μ = parameter that defines amount of compression vout = compressed output amplitude (volts)

( )

(max)(max)

ln 1

ln 1

inin

inout

vVV

vμ

μ

⎛ ⎞+⎜ ⎟⎜ ⎟

⎝ ⎠=+


Companding


PCM System with Companding


Delta Modulation PCMDelta Modulation Transmitter


Delta Modulation PCMDelta Modulation Receiver


Delta Modulation PCMAdaptive Delta Modulation


Points to remember

Modern communication systems are often mixture of analog and digital.Analog signal that is to be transmitted digitally must be quantized first.With PCM, more the bits used, greater is the accuracy, but higher are the bit rate and the channel bandwidth.Companding is used to increase accuracy without increasing the bit rate.

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Chapter 8 - PSAU · Prepared by Prof.V.K.Jain 15 Pulse Code Modulation (PCM) zIn PCM, the available range of signal is divided into N levels and each assigned a binary number. zEach