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This is the introduction to digital signal processing
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7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 1/21
6/19/20
SIGNAL
Is a function representing a physical quantity
or variable, and typically it contains
information about the behavior or nature of
the phenomenon.
SIGNAL
is represented as a function of an
independent variable t . t represents time.
is denoted by x ( t ).
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 2/21
6/19/20
Types of Signal
Analog or
Continuous-time
Digital or
Discrete-time
Continuous to Discrete
A discrete-time signal x[n] may be obtained by
SAMPLING a continuous-time signal x(t).
's are called samples
is the sampling interval
the arrow to denote the n = 0 term
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 3/21
6/19/20
= 0.25
= 0.5
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 4/21
6/19/20
= 1
Real and Complex Signal
• A signal x[n] is a Real Signal if its value is a real
number.
• A signal x[n] is a Complex Signal if its value is a
complex number.
where: = −1
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 5/21
6/19/20
Complex Signal
• Rectangular
• Polar
magnitude
phase
Even and Odd Signals
• A signal is referred to as even signal if
= −
• A signal is referred to as odd signal if
= − −
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 6/21
6/19/20
Even and Odd Signals
• Even Signal
Even and Odd Signal
• Odd Signal
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 7/21
6/19/20
Periodic and Aperiodic Signal
• Periodic Signal
Basic Discrete Signals
• Unit Step Sequence
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 8/21
6/19/20
Basic Discrete Signals
• Unit Impulse or Unit Sample Sequence
Basic Discrete Signals
• Real Exponential Sequence
=
= ω
ω = cos ω + ( ω )
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 9/21
6/19/20
Basic Discrete Signals
• Real Exponential Sequence
a>1
1>a>0
Basic Discrete Signals
• Real Exponential Sequence
0>a>-1
a<-1
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 10/21
6/19/20
Basic Discrete Signals
• Sinusoidal Exponential Sequence
= (ω + )
= (ω )
Basic Discrete Signals
• Sinusoidal Exponential Sequence
=π
6
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 11/21
6/19/20
Basic Discrete Signals
• Sinusoidal Exponential Sequence
= n2
Signal Transformation
Shifting
This is the transformation defined by
= − . If y = ( − ),
DELAY
If is shifted to the right by samples,
if is positive.
ADVANCEIf is shifted to the left by samples,
if is negative.
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 12/21
6/19/20
Shifting
Signal Transformation
Reversal
This transformation is given by
= − and simply involves "flipping"
the signal x with respect to the index .
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 13/21
6/19/20
Reversal
Signal Transformation
Time Scaling
This transformation is defined by
= ⇒ Down-sampling
= / ⇒ Up-sampling
where and are positive integers.
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 14/21
6/19/20
Time Scaling
Continuous-time signal x(t)
Sketch and label each of the following signals.a. x(t - 2) c. x(t/2)
b. x(2t) d. x ( - t )
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 15/21
6/19/20
x(t - 2)
x(2t)
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 16/21
6/19/20
x(t/2)
x( - t )
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 17/21
6/19/20
Discrete-time signal x [ n ]
Sketch and label each of the following signals.
a. x[n – 2] c. x [ - n ]
b. x[2n] d. x [ - n + 2]
x[n – 2]
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 18/21
6/19/20
x[2n]
x [ - n ]
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 19/21
6/19/20
x [ - n + 2]
Continuous-time signal x(t)
Sketch and label each of the following signals.
a. X(t – 2) c. x (- t)
b. X(t/2) d. x (- t + 2)
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 20/21
6/19/20
X( t - 2 )
X(t)
t-1 0 1 2 3 4
X( t/2 )
X(t)
t-1 0 1 2 3 4-2
7/18/2019 Introduction to Signals
http://slidepdf.com/reader/full/introduction-to-signals 21/21
6/19/20
X( - t )
X(t)
t-1 0 1 2 3 4-2
X( - t + 2 )
X(t)
t-1 0 1 2 3 4-2