PULSE CODE MODULATION

Prepared by Dr. Sangeeta Srivastava for the students of B. Sc Electronics (Hons.), IIIrd year, Rajdhani College. Dated March 2020. The following references have been used:

• Communication Systems by Singh and Sapre

• Communication Systems by Haykin and Moher

• Analog and Digital Communication by Singal

• And, the You tube link https://www.youtube.com/watch?v=YJmUkNTBa8s

Pulse Code Modulation: A Digital Modulation Technique

Pulse Code Modulation (PCM) is a digital modulation technique. Here, a special form of A/D conversion takes place. It consists of sampling, quantizing, and encoding.

• Sampling is the process by which samples of the signals are taken in conformity with the Sampling Theorem.

• Quantization is the process by which the sampled signals lying between say, Vmaxand Vmin are broken up into levels. Each level (quanta) is then assigned a single value. For example, a sampled signal lying between 0.5 V to 1.5 V will be assigned the value 1 V. Unless the sampled signal has the value 1 V, some error/ noise will be introduced due to the difference between the sampled value and the quantized value. This gives rise to Quantization Error/Noise.

• Encoding refers to the conversion of the quantized signal to digital form.

PULSE CODE MODULATION

Advantages of PCMRuggedness to transmission noise and interference; Efficient regeneration of the coded signal along the transmission path; Possibility of a uniform format for different kinds of baseband signals; Ease of implementing Time Division Multiplexing.Disadvantages of PCMIncreased Band Width; Increased system complexity.Applications of PCMIt is the standard form of digital audio in computers, compact discs, digital telephony and other digital telephony applications.

THE FUNDAMENTALS

A

B

CPulse Value(v) Quantized Value Encoded Value

A 3.8 4 100

B 1.2 1 001

C 5.7 6 110

(Pulses lying between -0.5V to 0.5V= Quantized to 0 V, Pulses lying between 0.5V to 1.5V= Quantized to 1V……..)

Analog Signal:Continuous valueContinuous time

Digital Signal:Encoded ValueDiscrete time

Discrete valueDiscrete time

PAM signal Quantization Coding PCM

Continuous value Discrete time

Encoded Signal for the Quantized Pulses

Effect of Transmission Noise on Encoded Pulses

ENCODING of QUANTIZED PULSES

THE PCM SYSTEM

PCM SYSTEM in DETAIL

PCM

QUANTIZATION

UNIFORM QUANTIZATION: The quantization levels(step size) are uniformly spaced over the complete input range.

NON-UNIFORM QUANTIZATION: The quantization levels (step size) vary according to the instantaneous value of the input signal.

UNIFORM QUANTIZATION

S

S

(Note that in this example, M=8 and n=3)

TYPES of UNIFORM QUANTIZATION

Midtread Uniform Quantizer

Midriser Uniform Quantizer

UNIFORM QUANTIZATION (Contd.)

https://www.youtube.com/watch?v=YJmUkNTBa8s

NON-UNIFORM QUANTIZATION: COMPANDING

Companding is the process of compressing the signal at the transmitter end and expanding itat the receiver end to achieve a uniform Signal to Noise ratio across all signal levels. As signalsget quantized according to their strengths, non-uniform quantization is said to take place.

Compression at the transmitter: Low level samples are amplified whereas the high-level samples are attenuated or compressed.

Expansion at the receiver: The compressed signals are expanded to recover the original sample values.

Companding

COMPRESSION TECHNIQUES

A Compressive Law

• Sending binary numbers directly through the channel seems to be the simplest option.• However, the resulting bit patterns might create an undesirable static voltage.• Therefore, Line Codes are used to eliminate the average static voltage and save power and perhaps even bandwidth.

ENCODING

0 volt

5 volt

averagestatic voltage

0 0000 0

1 1 1 1 1

• Unipolar signaling: 1 = +A volt, 0 = 0 volt• Polar signaling: 1 = +A volt, 0 = -A volt• Bipolar signaling: 1 = +A or –A, 0 = 0 volt(Also called the alternate mark inversion – AMI)

• Manchester signaling: 1 = +A (half duration) followed by –A (half duration)0 = -A (half duration) followed by +A (half duration)

• Differential Encoding: a binary value is denoted by a signal change rather than a particular signal state.

Additional combinations can be made along with RZ (return to zero) and NRZ (non return to zero).

TYPES of LINE CODE

Types of Line Code (Contd.)

Differential Encoding

Equalizer Decision Making Device

Timing Circuit

Distorted PCM signal

Regenerated PCM signal

• Equalization: Amplitude and Phase Distortions introduced in PCM signals are removed by reshaping the received distorted pulses.

• Timing Circuit: The circuit derives a periodic pulse train from the received pulses. These are used for sampling the equalized pulses at that instant where SNR is maximum.

• The Decision-Making Device: this device is enabled when the amplitude of the equalized pulses plus noise exceeds a predetermined threshold level.

REGENERATIVE REPEATER

As the PCM channels are bandlimited, the received waveforms are distorted as they extend in the next time slot. Resulting in error in determination of received bits. In PCM, adjacent time slots are generally symbols in code representation of a single quantized sample

INTERSYMBOL INTERFERENCE

NOISE IN PCM SYSTEMS

Two major sources of noise in PCM systems are:

A)Transmission Noise (may be introduced anywhere between the transmitter output and the receiver input)

B) Quantization Noise (is introduced in the transmitter and is carried along to the receiver output)

TRANSMISSION NOISE

A

B

C

𝑉"

𝑉"

Figure A shows the bits 101 that are transmitted. Figure B shows the distortion due to noise at the receiver end. All three bits X, Y, Z remain within the limits of the threshold voltage 𝑉". Therefore the correct code 101 is received. In Figure C, however, the X bit is received as a 0 and Y bit is received as a 1. The Z bit remains error free. The possibility of errors being introduced as in Fig. C is very low. And, can be minimized further by increasing the difference between the voltage levels of bit 1 and 0.

QUANTIZATION NOISE

Linear input-output transfer curve

Quantized signal Quantization Error

QUANTIZATION NOISE (CONTD.).

A single Quantization step in detail

Quantization Error 0

Quantization Error

2

22

2𝑡%

QUANTIZATION NOISE (CONTD.)

If the probability density distribution is uniform, then the mean square quantization error will be given by:

𝐸'() =∆𝑉 )

12

If the total number of levels be=𝑀And the peak to peak signal range varies between +𝑀 ⁄∆𝑉 2 to -𝑀 ⁄∆𝑉 2The total signal variation = 𝑀∆𝑉For a signal with a uniform probability distribution within this range, the mean square signal voltage is given by:

𝐸%) =𝑀∆𝑉 )

3

Therefore, the Signal to Noise ratio (SNR) will be given by:

𝑆𝑁𝑅 =𝐸6)

𝐸'()= 4𝑀)

As, 𝑀 = 2', where n is the total number of bits per code word,𝑆𝑁𝑅 = 4×2)'

In Decibels, the SNR will be given by:

𝑆𝑁𝑅9: = 10𝑙𝑜𝑔4 + 20𝑙𝑜𝑔𝑀 dB𝑆𝑁𝑅9: = 10𝑙𝑜𝑔4 + 20𝑙𝑜𝑔2' = (6 + 6𝑛) 𝑑𝐵

It may be noted that the constant 6 is dependent on the quantizationtechnique being used. Dependence of the SNR on the number of bits n implies that the SNR will be improved by increasing n. Of course, increasing Mor n is a tradeoff with the resultant increased system complexity.

QUANTIZATION NOISE (CONTD.)

BANDWIDTH OF TDM- PCM SYSTEM

Let, the number of channels bandlimited to 𝑓H = 𝑁

And the length of PCM code or the number of bits per code word=n

Now, the Sampling Frequency=2𝑓HHz

Therefore, the Sampling Time= ⁄1 2𝑓H sec

So, the total number of bits per sampling period including the synchronizingbit=𝑛𝑁 + 1

The Bit Duration=𝑇: =6JHKLM'N OPQMR9

"RSJL 'THUPQ RV UMS%= W

)VX 'YZWsec

Therefore, the Bandwidth𝐵𝑊 = 2𝑓H 𝑛𝑁 + 1 ≈ 2𝑓H𝑛𝑁 Hz