4.2 Digital Transmission

Outlines

□ Pulse Modulation□ Pulse Code Modulation□ Delta Modulation□ Line Codes

□Sampling analog information signal□Converting samples into discrete pulses□Transport the pulses from source to

destination over physical transmission medium.

Cont’d...□Four (4) Methods

1. PAM2. PWM3. PPM4. PCM

Analog Pulse Modulation

Digital Pulse Modulation

Cont’d...□ Analog Pulse Modulation

□ Carrier signal is pulse waveform and the modulated signal is where one of the carrier signal’s characteristic (either amplitude, width or position) is changed according to information signal.

• The amplitude of pulses is varied in accordance with the information signal.• Width & position constant.

Pulse Amplitude Modulation (PAM)

Pulse Width Modulation (PWM)

□Sometimes called Pulse Duration Modulation (PDM).

□The width of pulses is varied in accordance to information signal.

□Amplitude & position constant.

Cont’d...

• Modulation in which the temporal positions of the pulses are varied in accordance with some characteristic of the information signal.

• Amplitude & width constant.

Pulse Position Modulation (PPM)

Advantages & Drawbacks of Pulse Modulation

□ Noise immunity.□ Relatively low cost digital

circuitry.□ Able to be time division

multiplexed with other pulse modulated signal.

□ Storage of digital streams.□ Error detection &

correction

□ Requires greater BW to transmit & receive as compared to its analog counterpart.

□ Special encoding & decoding methods must be used to increased transmission rates & more difficult to be recovered.

□ Requires precise synchronization of clocks between Tx & Rx.

Sampling □A process of taking samples of information

signal at a rate of Nyquist’s sampling frequency.

□Nyquist’s Sampling Theorem :The original information signal can be reconstructed at the receiver with minimal distortion if the sampling rate in the pulse modulation

system equal to or greater than twice the maximum information signal frequency.

fs >= fm (max)

Cont’d...□Two basic techniques used to

perform the sampling function:□Natural sampling□Flat-top sampling

Natural Sampling□Tops of the sample pulses retain their

natural shape during the sample interval.□Frequency spectrum of the sampled

output is different from an ideal sample.□Amplitude of frequency components

produced from narrow, finite-width sample pulses decreases for the higher harmonics □Requiring the use of frequency equalizers

Natural Sampling

Flat-top Sampling□Common used in PCM systems.□Accomplish in a sample-and-hold circuit

□To periodically sample the continually changing analog input voltage & convert to a series of constant-amplitude PAM voltage levels.

□The input voltage is sampled with a narrow pulse and then held relatively constant until the next sample is taken.

Cont’d…□Sampling process alters the frequency

spectrum & introduces aperture error.□The amplitude of the sampled signal

changes during the sample pulse time.□Advantages:

□Introduces less aperture distortion □Can operate with a slower ADC

Flat-top Sampling

□Basic scheme of PCM system□Quantization□Quantization Error□Companding□Block diagram & function of TDM-PCM

communication system

Basic scheme of PCM system□The most common technique for using

digital signals to encode analog data is PCM.

□Example: To transfer analog voice signals off a local loop to digital end office within the phone system, one uses a codec.

Cont’d...□Because voice data limited to frequencies

below 4000 Hz, a codec makes 8000 samples/sec. (i.e., 125 microsecond/sample).

□If a signal is sampled at regular intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal.

PCM Block Diagram

• Most common form of analog to digital modulation• Four step process

1. Signal is sampled using PAM (Sample)

2. Integer values assigned to signal (PAM)

3. Values converted to binary (Quantized)

4. Signal is digitally encoded for transmission (Encoded)

4 Steps Process

Cont’d…□ Analog signal is sampled.□ Converted to discrete-time continuous-amplitude signal (Pulse Amplitude Modulation)

□ Pulses are quantized and assigned a digital value.□ A 7-bit sample allows 128 quantizing levels.

□ PCM uses non-linear encoding, i.e., amplitude spacing of levels is non-linear□ There is a greater number of quantizing steps for low amplitude□ This reduces overall signal distortion.

□ This introduces quantizing error (or noise).□ PCM pulses are then encoded into a digital bit stream.□ 8000 samples/sec x 7 bits/sample = 56 Kbps for a single voice

channel.

PCM Example

Quantization□ A process of converting an infinite number of possibilities to

a finite number of conditions (rounding off the amplitudes of flat-top samples to a manageable number of levels).

Cont’d...

Analog input signal

Sample pulse

PAM signal

PCM code

The quantization interval @ quantum = the magnitude difference between adjacent steps.

The resolution = the magnitude of a quantum = the voltage of the minimum step size.

The quantization error = the quantization noise = ½ quantum = (orig. sample voltage – quantize

level)

PCM code = (sample voltage/resolution)

Cont’d…

□ A difference between the exact value of the analog signal & the nearest quantization level.

QUANTIZATION ERROR

Types of Quantization

Midtread Midrise

Types of Quantizer1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.

Dynamic Range (DR)□ Largest possible magnitude/smallest possible magnitude.

□ Where □ DR = absolute value of dynamic range□ Vmax = the maximum voltage magnitude□ Vmin = the quantum value (resolution)□ n = number of bits in the PCM code

resolutionV

VVDR max

min

max

12 nDR)log(20)( DRdBDR

Example 11. Calculate the dynamic range for a

linear PCM system using 16-bit quantizing.

2. Calculate the number of bits in PCM code if the DR = 192.6 dB

Coding Efficiency□A numerical indication of how

efficiently a PCM code is utilized.□The ratio of the minimum number of

bits required to achieve a certain dynamic range to the actual number of PCM bits used.

Coding Efficiency = Minimum number of bits x 100

Actual number of bits

Signal to Quantization Noise Ratio (SQR)

□ The worst-case voltage SQR

□ SQR for a maximum input signal

□ The signal power-to-quantizing noise power ratio

eQresolutionSQR (min)

eQVSQR max

(max)

12

2

12

)(

22

2

log10)(

log10

power noiseon quantizati averagepower signal averagelog10

qqR

v

dB

v

R

SQR

R =resistance (ohm)

v = rms signal voltage

q = quantization interval

Example 21. Calculate the SQR (dB) if the input signal = 2

Vrms and the quantization noise magnitudes = 0.02 V.

2. Determine the voltage of the input signals if the SQR = 36.82 dB and q =0.2 V.

Effect of Non-Linear Coding

Nonlinear Encoding

□ Quantization levels not evenly spaced

□ Reduces overall signal distortion

□ Can also be done by companding

Companding• The process of compressing and then expanding.

• The higher amplitude analog signals are compressed

prior to transmission and then expanded in receiver.

• Improving the DR of a communication system.

Companding Functions

Method of Companding□ For the compression, two laws are adopted: the -law in

US and Japan and the A-law in Europe.

□ -law□

□ A-law

□ The typical values used in practice are: =255 and A=87.6.□ After quantization the different quantized levels have to

be represented in a form suitable for transmission. This is done via an encoding process.

)1ln()1ln(

maxmax

VV

out

inVV

11ln1

)ln(1

10ln1

max

maxmax

out

inVV

out

inVV

out

VV

AAA

AVV

AA

VV

in

in

Vmax= Max uncompressed analog input voltage

Vin= amplitude of the input signal at a particular of instant time

Vout= compressed output amplitude

A, = parameter define the amount of compression

Example 3 □A companding system with µ = 255

used to compand from 0V to 15 V sinusoid signal. Draw the characteristic of the typical system.

□Draw an 8 level non-uniform quantizer characteristic that corresponds to the mentioned µ.

Cont’d...

μ-law A-law

PCM Line Speed

□ The data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line.

□ Where□Line speed = the transmission rate in bits per

second□Sample/second = sample rate, fs

□Bits/sample = no of bits in the compressed PCM code

samplebitsX

secondsamples speed line

Example 4□For a single PCM system with a

sample rate fs = 6000 samples per second and a 7 bits compressed PCM code, calculate the line speed.

Virtues & Limitation of PCM

The most important advantages of PCM are:□Robustness to channel noise and

interference.□Efficient regeneration of the coded

signal along the channel path.□Efficient exchange between BT and SNR.□Uniform format for different kind of

base-band signals.□Flexible TDM.

Cont’d…□Secure communication through the use of

special modulation schemes of encryption.□These advantages are obtained at the cost of

more complexity and increased BT.□With cost-effective implementations, the cost

issue no longer a problem of concern.□With the availability of wide-band

communication channels and the use of sophisticated data compression techniques, the large bandwidth is not a serious problem.

Time-Division Multiplexing

□This technique combines time-domain samples from different message signals (sampled at the same rate) and transmits them together across the same channel.

□The multiplexing is performed using a commutator (switch). At the receiver a decommutator (switch) is used in synchronism with the commutator to demultiplex the data.

Cont’d…□ TDM system is very sensitive to symbol

dispersion, that is, to variation of amplitude with frequency or lack of proportionality of phase with frequency. This problem may be solved through equalization of both magnitude and phase.

□ One of the methods used to synchronize the operations of multiplexing and demultiplexing is to organize the multiplexed stream of data as frames with a special pattern. The pattern is known to the receiver and can be detected very easily.

Block diagram of TDM-PCM communication system