Lecture 10:
Quantizing & PCM
1nd semester 1439-2017
By: Adal ALashban
1
Introduction
- A digital signal is superior to an analog signal
because it is more robust to noise and can easily
be recovered, corrected and amplified.
- For this reason, the tendency today is to change an
analog signal to digital data.
- Changing analog signal to digital signal:
Sampling  Quantizing
2
3
Quantization
- In order to process the sampled signal digitally, the
sample values have to be quantized to a finite
number of levels, and each value can then be
represented by a string of bits.
- To quantize a sample value is to round it to the
nearest point among a finite set of permissible
values.
- Therefore, a distortion will inevitably occur. This is
called quantization noise (or error).
4
Quantization
5
Modulation
Continuous wave (CW) modulation
Pulse Modulation
Angle
modulation
AM
FM
Analog Pulse
Modulation
Digital Pulse
Modulation
PM
PAM
PPM
PDM
DM
PCM
6
Pulse-code Modulation (PCM)
- Pulse-code Modulation (PCM), like PAM, is a
digital communication technique that sends
samples of the analog signal taken at a
sufficiently high rate.
- PCM differs than PAM in that it quantizes the
samples by constraining them to only take a
limited number of values, and then converts each
value into a binary string of bits that are
transmitted on the communication line.
7
Pulse-code Modulation (PCM)
- PCM consists of three steps to digitize an analog signal:
1. Sampling
2. Quantization
3. Binary encoding
- Before we sample, we have to filter the signal to limit
the maximum frequency of the signal as it affects the
sampling rate.
- Filtering should ensure that we do not distort the signal,
i.e. remove high frequency components that affect the
signal shape.
8
Components of PCM Encoder
9
Sampling
- Analog signal is sampled every Ts secs.
- Ts is referred to as the sampling interval or period.
- fs = 1/Ts is called the sampling rate or sampling
frequency.
- The process is referred to as pulse amplitude
modulation PAM and the outcome is a signal with
analog (non integer) values.
10
Note
- According to the Nyquist theorem,
the sampling rate must be at least 2 times the
highest frequency contained in the signal.
11
12
Recovery of a sampled sine wave for different
sampling rates
13
Quantization
- Sampling results in a series of pulses of varying
amplitude values ranging between two limits: a min
and a max.
- The amplitude values are infinite between the two limits.
- We need to map the infinite amplitude values onto a
finite set of known values.
- This is achieved by dividing the distance between min
and max into L zones, each of height height
 = (max - min)/L
14
15
Quantization Levels
- The midpoint of each zone is assigned a value from
0 to L-1 (resulting in L values)
n
16
- Each sample falling in a zone is then approximated
to the value of the midpoint.
3
2
1
0
n
approximating the value of the sample amplitude to the
quantized values.
17
Assigning Codes to Zones
- Each zone is then assigned a binary code.
- The 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:
nb = log2 L
- Given our example, nb = 2
- The 4 zone (or level) codes are therefore: 00, 01,
10, 11
18
Assigning Codes to Zones
11
10
01
00
3
2
1
0
Each zone is assigned a binary code
n
19
Assigning Codes to Zones
Use one of the line code scheme to get the digital signal
20
Thank You
21