Digital Signal Processing
Lecture-2
Signal Sampling and Quantization
1

Agenda
2
Sampling of Continuous Signal
Signal Reconstruction
Analog-to-Digital
Conversion,
Digital-to-
Analog Conversion, and Quantization
Summary
Li Tan and Jean Jiang, “DSP Fundamentals and Applications”,
2
nd
Edition, 2013, Elsevier.

Sampling of Continuous Signal
3

Sampling of Continuous Signal
4
Figure 1:
A digital signal processing scheme.
Figure 1 describes a simplified block diagram of a
digital signal processing (DSP) system.
Li Tan and Jean Jiang, “DSP Fundamentals and Applications”,
2
nd
Edition, 2013, Elsevier.

Just what does an A/D converter
DO?
Converts analog signals into binary words

Concept of Sampling
The analog filter processes the analog
input to obtain the band-limited signal,
which is sent to the analog-to-digital
conversion ADC unit
The ADC unit samples the analog signal,
quantizes the sampled signal, and
encodes the quantized signal levels to
the digital signal.

A simple ADC

Why Sampling?
Impossible to digitize an infinite
number of points because it
requires infinite amount of
memory and infinite amount of
processing power for
computations.
Sampling can solve such a
problem by taking samples at
the fixed time interval, as shown
in figures, where the time
T
represents the sampling interval
or sampling period in seconds.
This process is called
sample
and hold
. Since there exists
one
amplitude level for each
sampling interval.

Sampling Rate
For a given sampling interval T, which is
defined as the time span between two
sample points, the sampling rate is
therefore given by:
For example,
if a sampling period is T =125
µs, the sampling rate is determined as fs
=1/125 µs = 8,000 samples per second (Hz).
T
f
s
1

Sampling Rate
After the analog signal is sampled, we obtain the
sampled signal whose amplitude values are taken
at the sampling instants,
thus the processor is able
to handle the sample points
.
Next, we have to ensure that
samples are collected
at a rate high enough that the original analog
signal can be reconstructed or recovered later
.
In other words, we are looking for a
minimum
sampling rate to acquire a complete
reconstruction of the analog signal from its
sampled version
.

Aliasing
If an analog signal is not appropriately
sampled,
aliasing
will occur, which causes
unwanted signals in the desired frequency
band.
The
sampling theorem
guarantees that an
analog signal can be in theory perfectly
recovered as long as the sampling rate is
at
least twice as large as the highest-frequency
component of the analog signal to be
sampled
. The condition is described as:
max
2
f
f
s

Sampling Theorem Concept (Cont…)
Here,
f
max
is the maximum-frequency
component of the analog signal to be
sampled.

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