Convolution Integral
Linear time-invariant
circuit represented by
block
h(t) impulse response of
circuit
x(t) input excitation signal
y(t) output desired signal
Y(s) = H(s).X(s)
y(t) = h(t) * x(t) = x(t) * h(t)
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Convolution Integral-Electrical Circuit Analysis-Lecture Slides, Slides of Electrical Circuit Analysis
This lecture is part of lecture series on Electrical Circuit Analysis course. It was delivered by Prof. Mursleen Sayed at Bengal Engineering and Science University. It includes: Convolution, Integral, Linear, Time, Invariant, Excitation, Impulse, Response, Input, Output
Typology: Slides
2011/2012
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Convolution Integral
Linear time-invariantcircuit represented byblock
h(t) impulse response ofcircuit
x(t) input excitation signal
y(t) output desired signal
Y(s) = H(s).X(s)
y(t) = h(t) * x(t) = x(t) * h(t)
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Convolution Integral
Convolution Integral relates the output y(t) of alinear time-invariant circuit to the input x(t) of thecircuit and the circuit’s impulse response h(t)
The convolution integral is used to extract theresponse of a circuit to an arbitrary source
It allows evaluation of x(t) and h(t) in time domain,where x(t) and h(t) are known through experimentaldata
λ d ) λ ( x ) λ t ( h λ d ) λ t ( x ) λ ( h ) t ( y
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Example
h(
) = e
u(
v
i^
= 4t
for 0
t
v
(i
for 0
v
(-i
for -
v
(t-i
)= 4(t-
for t-
t
λ
λ e
λ
λ
λ
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Example
For 0
t
20 0
λ
x(t- )
λ
5
10
t-
t-
5 t 0
20 0
λ
x(t- )
λ
5
10
t-
t-
10 t 5
20 0
λ
x(t- )
λ
5
10
t-
t-
t 10
t
t
t
t 0
λ
o
λ d e ) λ t ( 4 v ) 1 t e ( 4 v
t
o
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Example
t^
vo
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
) 1 t e ( 4 v
t
o
) e e 5 ( 4 v ) 5 t ( t o
) e 5 e e ( 4 v ) 10 t ( ) 5 t ( t o
5.00 0. 25.0020.00 15.0010.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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Graphic Interpretation of theConvolution Integral
λ
λ
λ
λ
τ^1
τ^2
λ
τ^1
τ^2
λ
λ
τ^1
τ^2
λ
λ
τ^1 λ λ
λ
λ
λ
λ
τ^1
τ^2
λ
λ
λ
λ
λ
τ^1
λ^
λ
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