Signals and Systems: Unit 1
Introduction to Continuous and Discrete time signals
Dr. Pritesh Shah
pritesh.shah@sitpune.edu.in
Department of Electronics & Telecommunication Engineering,
Symbiosis Institute of Technologly, Pune
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Classification of Signals
Unit 1: Introduction to Continuous and
Discrete time signals
Lecture 10
Classification of Signals
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Classification of Signals
Energy and Power Signal
A signal is said to be energy signal when it has finite energy. For an
energy signal, average power P = 0.
Z ∞
E= |x(t)|2 dt (1)
−∞
A signal is said to be power signal when it has finite power. For a
power signal, total energy E = ∞. Periodic signals are example of
power signals.
Z T
1
P = lim |x(t)|2 dt (2)
T →∞ 2T −T
The signals that don’t satisfy the above properties are neither energy
nor power signals.
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Classification of Signals
Energy and Power Signal
The power of the energy signal is zero over infinite time.
The energy of the power signal is infinite over infinite time.
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Classification of Signals
Energy and Power Signal
Example 01
Determine the power of the signal x(t) = A sin (ω0 t + θ).
Average Power,
Z T
1
P = lim |x(t)|2 dt (3)
T →∞ 2T −T
Z T
1
P = lim |A sin (ω0 t + θ)|2 dt (4)
T →∞ 2T −T
A2 T 1 − cos(2ω0 t + 2θ)
Z
P = lim dt (5)
T →∞ 2T −T 2
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Classification of Signals
Energy and Power Signal
Example 01
Determine the power of the signal x(t) = A sin (ω0 t + θ).
Average Power,
T T
A2 A2
Z Z
P = lim dt − lim cos (2ω0 t + 2θ)dt (6)
T →∞ 4T −T T →∞ 4T −T
T
A2
Z
P = lim dt − 0 (7)
T →∞ 4T −T
A2 A2 A2
P = lim [T + T ] = lim [2T ] = (8)
T →∞ 4T T →∞ 4T 2
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Classification of Signals
Energy and Power Signal
Example 02 (a)
Determine the power of the signals.
(a) x(t) = 7 cos (20t + π3 )
72
Power = = 24.5 W
2
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Classification of Signals
Energy and Power Signal
Example 02 (b)
Determine the power of the signals.
(b) x(t) = 2 cos (20t + π4 ) + 3 sin (30t + π2 )
22 32
Power = + = 6.5 W
2 2
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Classification of Signals
Energy and Power Signal
Example 02 (c)
Determine the power of the signals.
(c) x(t) = 6 cos 4t cos 8t
6
x(t) = 6 cos 4t cos 8t = [cos 12t + cos 4t]
2
x(t) = 3 cos 12t + 3 cos 4t
32 32
Power = + =9W
2 2
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Classification of Signals
Energy and Power Signal
Example 02 (d)
Determine the power of the signals.
(d) x(t) = e j2t cos 6t
x(t) = e j2t cos 6t = (cos 2t + j sin 2t) cos 6t
1
x(t) = cos 2t cos 6t +j sin 2t cos 6t = [(cos 8t +cos 4t)+j((sin 8t −sin 4t)]
2
(1/2)2 (1/2)2 (1/2)2 (1/2)2 1
Power = + + + = W
2 2 2 2 2
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Classification of Signals
Energy and Power Signal
Example 02 (e)
Determine the power of the signals.
(d) x(t) = Ae j2t
x(t) = Ae j2t = A(cos 2t + j sin 2t)
A2 A2
Power = + = A2 W
2 2
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