notes

1. 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

2. 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 SamplingTheorem.
• Quantization is the process by which the sampled signals lying between say, Vmax
and Vmin are broken up into levels. Each level (quanta) is then assigned a single
value. For example, a sampled signal lying between 0.5V to 1.5V will be assigned
the value 1V. Unless the sampled signal has the value 1V, 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.

3. PULSE CODE MODULATION
Advantages of PCM
Ruggedness 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 implementingTime Division Multiplexing.
Disadvantages of PCM
Increased BandWidth; Increased system complexity.
Applications of PCM
It is the standard form of digital audio in computers, compact
discs, digital telephony and other digital telephony
applications.

4. THE FUNDAMENTALS
A
B
C
Pulse 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 0V,
Pulses lying between 0.5V to 1.5V= Quantized to 1V……..)
Analog Signal:
Continuous value
Continuous time
Digital Signal:
Encoded Value
Discrete time
Discrete value
Discrete time
PAM signal Quantization Coding PCM
Continuous value
Discrete time

5. Encoded Signal for the Quantized Pulses
Effect of Transmission Noise on Encoded Pulses
ENCODING of QUANTIZED PULSES

6. THE PCM SYSTEM

7. PCM SYSTEM in DETAIL
PCM

8. 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.

9. UNIFORM QUANTIZATION
S
S
(Note that in this example, M=8 and n=3)

10. TYPES of UNIFORM QUANTIZATION
Midtread Uniform
Quantizer
Midriser Uniform
Quantizer

11. UNIFORM QUANTIZATION (Contd.)
https://www.youtu
be.com/watch?v=
YJmUkNTBa8s

12. NON-UNIFORM QUANTIZATION: COMPANDING
Companding is the process of compressing the signal at the transmitter end and expanding it
at the receiver end to achieve a uniform Signal to Noise ratio across all signal levels. As signals
get 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

13. COMPRESSION TECHNIQUES
A Compressive Law

14. • 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
average
static voltage
0 0
0
0
0 0
1 1 1 1 1

15. • 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

16. Types of Line Code
(Contd.)
Differential Encoding

17. 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

18. 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

19. 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)

20. 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.

21. QUANTIZATION NOISE
Linear input-output transfer curve
Quantized signal Quantization Error

22. QUANTIZATION NOISE (CONTD.)
.
A single Quantization step in detail
Quantization
Error 0
Quantization Error
2
2
2
2
𝑡%

23. 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=𝑀
And the peak to peak signal range varies between +𝑀 ⁄
∆𝑉 2 to -𝑀 ⁄
∆𝑉 2
The total signal variation = 𝑀∆𝑉
For 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)'

24. In Decibels, the SNR will be given by:
𝑆𝑁𝑅9: = 10𝑙𝑜𝑔4 + 20𝑙𝑜𝑔𝑀 dB
𝑆𝑁𝑅9: = 10𝑙𝑜𝑔4 + 20𝑙𝑜𝑔2'
= (6 + 6𝑛) 𝑑𝐵
It may be noted that the constant 6 is dependent on the quantization
technique 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 M
or n is a tradeoff with the resultant increased system complexity.
QUANTIZATION NOISE (CONTD.)

25. 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 SamplingTime= ⁄
1 2𝑓H sec
So, the total number of bits per sampling period including the synchronizing
bit=𝑛𝑁 + 1
The Bit Duration=𝑇: =
6JHKLM'N OPQMR9
"RSJL 'THUPQ RV UMS%
=
W
)VX 'YZW
sec
Therefore, the Bandwidth
𝐵𝑊 = 2𝑓H 𝑛𝑁 + 1 ≈ 2𝑓H𝑛𝑁 Hz