CHAPTER ONE
INTRODUCTION TO DIGITAL SIGNAL PROCESSING
By: Yibeltal A.
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INTRODUCTION
Digital signal processing is an area of science and engineering that has developed rapidly
over the past 30 years.
The rapid developments in integrated-circuit technology, starting:
With medium-scale integration (MSI)
progressing to large-scale integration (LSI),
And now, very-large-scale integration (VLSI) of electronic circuits has encouraged
the development of:
Powerful, Smaller, Faster and cheaper digital computers and special-
purpose digital hardware.
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These inexpensive and relatively fast digital circuits have made it possible to
construct highly sophisticated digital systems.
Capable of performing complex digital signal processing functions and tasks,
which are usually to difficult too expensive to be performed by analog signal
processing systems.
Many of the signal processing tasks that were conventionally performed by
analog means are realized today by less expensive and often more reliable
digital hardware.
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Signals, Systems, and Signal Processing
Signals: is defined as any physical quantity that varies with time, space, or any other
independent variable or variables. Mathematically, we describe a signal as a function of
one or more independent variables.
Example: (1.1)
(1.2)
Describe two signals, one that varies linearly with the independent variable t(time) and a
second that varies quadratically with t.
(1.3)
This function describes a signal of two independent variables x and y that could represent
the two spatial coordinates in a plane.
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Example1: Temperature over time t, brightness (luminance) of an image over (x; y), pressure
of a sound wave over (x; y; z) or (x; y; z; t) Speech signal:
Example2: pressure as a function of altitude, sound as a function of time, color as
a function of space, ……
(1.4)
System: is a physical device that performs an operation on a signal
Examples: Analog amplifier, noise canceller, communication Channel, transistor, filter
For example: a filter use to reduce the noise and interférence corrupting a desired
information- bearing signal. In this case the filter performés some operations on the signal
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In General if the operation is linear, then the system is called linear and if the
operation is non linear, the system is said to be nonlinear.
How is a System Represented?
A system takes a signal as an input and transforms it into another signal
Input signal Output signal
System
x(t) y(t)
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Types of Systems
Causal & Non-causal
Linear & Non Linear
Time Variant &Time-invariant
Stable & Unstable
Static & Dynamic
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Signal processing
Signal Processing involves modifying, analyzing and synthesizing to
pull meaning out of it
Analog signal processing: deals with transformation of analog signals
Processing is done using electrical networks consisting of active and
passive elements
Digital signal processing: deals with the processing of discrete signals
Processing is done using general purpose computer, ASICS, EPGAs, DSP
chips etc…
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Basic Elements of a Digital signal processing system
Most of the signal encountered in science and engineering are analog in nature
The signals are functions of a continuous variable, such as time or space and values in a
continuous range
Signals can be processed directly by appropriate analog systems
Analog Analog
Analog
signal output signal
input signal
processor
Figure 1.1: Block diagram of analog signal processing system
Digital signal processing provides an alternative method for processing the analog
signal to perform the process digitally
The convertor which interface between analog to digital is called analog-to-digital
(A/D)
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The output of the A/D convertor is a digital signal that is appropriate as an input to the
digital processor.
The digital output from the digital signal processor is to the user in analog form.
The interface between digital to analog is called Digital-to-Analog (D/A) convertor
Analog A/D D/A Analog
DSP
input signal convertor convertor output signal
Digital Digital
input signal output signal
Figure 1.2: Block diagram of a digital signal processing system
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Advantages of digital signal processing
System allows flexibility in reconfiguring
More Accuracy
Signals are easily stored on magnetic media without loss of signal fidelity
Easily applied in practical systems
Digital implementation of signal processing system is cheaper
It allows the implementation of more sophisticated signal processing algorithms
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Disadvantages of DSP
• Higher power consumption
• Higher learning curve is required for operation
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Application of DSP
• Speech and audio processing
• Image and video processing
• Military and telecom
• Consumer electronics
• Healthcare and Biomedical sectors
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Classification of Signals
Deterministic vs. Random Signals
Deterministic signal:
Any signal that can be uniquely described by an explicit mathematical
expression, a table of data, or a well-defined rule
All past, present and future values of the signal are known precisely without
any uncertainty
Random signal:
Any signal that lacks a unique and explicit mathematical
It may not be possible to accurately describe the signal
The deterministic model of the signal may be too complicated to be of use.
These signals can’t be expressed mathematically
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Continuous-Time vs. Discrete-Time Signals
Continuous-Time Signals:
signals take on real or complex values as a function of an independent variable
that ranges over the real numbers and are denoted as x( t ) .
Signal is defined for every value of time in a given interval (a, b) where (a ≥ -∞)
and (b ≤ ∞).
Examples: voltage as a function of time, height as a function of pressure….
Discrete-Time Signals:
Signal is defined only for certain specific values of time; typically taken to be
equally spaced points in an interval.
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signals take on real or complex values as a function of an independent variable
that ranges over the integers and are denoted as x[n]
Examples: number of stocks traded per day, average income per province.
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Sampling and Quantization
• Sampling :The process of measuring the instantaneous values of continuous-time signal in a
discrete form.
• To discretize the signals, the gap between the samples should be fixed. That gap can be
termed as a sampling period Ts.
• Sampling frequency is the reciprocal of the sampling period
Sampling frequency=fs=1/Ts
• This sampling frequency, can be simply called as Sampling rate.
• The sampling rate denotes the number of samples taken per second
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Cont.…
• Suppose that a signal is band-limited with no frequency components
higher than W Hertz.
• That means, W is the highest frequency. For such a signal, for effective
reproduction of the original signal, the sampling rate should be twice
the highest frequency. Which means,
fs= 2W
Where
fs is the sampling rate
W is the highest frequency
• This rate of sampling is called as Nyquist rate.
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Quantization
• is a process of assigning the analog signal samples to a pre- determined discrete
levels. The number of quantization levels ,L, depends on the number of bits per
sample, n, used to code the signal
The magnitude of the minimum step size of the quantization levels is called resolution,
∆V
It is equal in magnitude to the voltage of the least significant bit of the magnitude
step size of the digital to analog converter (DAC).
• The resolution depends on the maximum voltage, Vmax, and the minimum voltage
Vmin of the information signal, where
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