Introduction to Signals
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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 ).
description
This is the introduction to digital signal processing
Transcript of Introduction to Signals
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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 ).
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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
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= 0.25
= 0.5
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= 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
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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
= − −
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Even and Odd Signals
• Even Signal
Even and Odd Signal
• Odd Signal
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Periodic and Aperiodic Signal
• Periodic Signal
Basic Discrete Signals
• Unit Step Sequence
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Basic Discrete Signals
• Unit Impulse or Unit Sample Sequence
Basic Discrete Signals
• Real Exponential Sequence
=
= ω
ω = cos ω + ( ω )
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Basic Discrete Signals
• Real Exponential Sequence
a>1
1>a>0
Basic Discrete Signals
• Real Exponential Sequence
0>a>-1
a<-1
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Basic Discrete Signals
• Sinusoidal Exponential Sequence
= (ω + )
= (ω )
Basic Discrete Signals
• Sinusoidal Exponential Sequence
=π
6
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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.
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Shifting
Signal Transformation
Reversal
This transformation is given by
= − and simply involves "flipping"
the signal x with respect to the index .
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Reversal
Signal Transformation
Time Scaling
This transformation is defined by
= ⇒ Down-sampling
= / ⇒ Up-sampling
where and are positive integers.
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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 )
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x(t - 2)
x(2t)
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x(t/2)
x( - t )
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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]
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x[2n]
x [ - n ]
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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)
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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
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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
