FUNDAMENTAL DSP CONCEPTS
C. Williams & W. Alexander
North Carolina State University, Raleigh, NC (USA)
ECE 513, Fall 2016
C. Williams & W. Alexander (NCSU)
FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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Outline
1
Introduction
2
Digital Signal Processing Applications
3
Why Digital Signal Processing
4
Representation of Discrete–Time Signals
5
Operations on Sequences
6
Normalized Frequency Representation
7
The Z–Transform
8
Region of Convergence
9
Frequency Representation of Discrete–Time Systems
10
Difference Equation Representation
11
The Frequency Response
12
Pole–Zero Plots
13
System Response
14
Frequency Shifting
15
Inverse Z–Transform for Systems with Complex Poles
16
Inverse Z–Transform for Systems with Multiple Poles
17
Cascade Implementation of Digital Filters
18
Stabilization of an Unstable Filter
19
References
C. Williams & W. Alexander (NCSU)
FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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Introduction
Signals play an important role in many activities in our daily lives.
Examples include:
Speech
Music
Biomedical signals
Video
Digital Television
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FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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Introduction
A deterministic signal
is a function of an independent variable such as time, distance,
position, temperature, and pressure. It
can be uniquely determined by
a well-defined process such as a mathematical expression of one or
more independent variables,
or by table look up.
For example,
s
(
t
) =
3 sin
(
2
.
1
π
t
+
0
.
3198
)
u
(
t
)
(1)
is a deterministic signal with independent variable
t
.
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FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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Introduction
A speech signal can not be described functionally by a
mathematical expression.
However, a recorded segment of speech can be represented to a
high degree of accuracy as the sum of several sinusoids of
different amplitudes and frequencies such as [1]
s
(
t
) =
N
k
=
1
A
k
(
t
)
sin
[
2
π
F
k
(
t
)
t
+
θ
k
(
t
)]
(2)
A signal that is determined in a random way and can not be
predicted ahead of time is a random signal.
Statistical approaches are often used to analyze random signals.
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FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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DSP Applications
Digital signal processing is heavily used in information technology.
Information technology includes such diverse subjects as
digital signal processing,
image processing,
multimedia applications,
computational engineering,
visualization of data,
database management,
teleconferencing,
remote operation of robots,
autonomous vehicles,
computer networks, etc.
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FUNDAMENTAL DSP CONCEPTS
ECE 513, Fall 2016
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Why DSP?
Many applications involving continuous–time signals use digital
signal processing.
This often involves
1
sampling the continuous–time signal at regular intervals,
2
quantizing the samples to obtain a digital sequence,
3
processing the digital system using a computer or a digital system,
4
converting the output digital sequence to a continuous–time
system.