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This is solution to problems related Electrical Circuit Analysis course. It was given by Prof. Gurnam Kanth at Punjab Engineering College. Its main points are: Fourier, Transform, Signal, Waveform, Signal, MATLAB, Coefficients, Amplitude, Phase, Spectra
Typology: Exercises
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Chapter 18, Problem 1.
Obtain the Fourier transform of the function in Fig. 18.26.
Figure 18.
For Prob. 18.1.
Chapter 18, Solution 1.
f '(t)=δ(t+ 2 )−δ(t+ 1 )−δ(t− 1 )+δ(t− 2 )
j 2 j j j 2 j F( ) e e e e
ω ω −ω −ω ω ω = − − +
= 2 cos 2 ω− 2 cos ω
F(ω) = ω
ω− ω
j
2 [cos 2 cos ]
Chapter 18, Problem 2.
Figure 18.
For Prob. 18.2.
Chapter 18, Solution 2.
0 , otherwise
t, 0 t 1 f(t)
f"(t) = δ(t) - δ(t - 1) - δ'(t - 1)
Taking the Fourier transform gives
2 F(ω) = 1 - e
-jω
-jω
F(ω) = (^) 2
j ( 1 j )e 1
ω
ω
or
−ω ω =
1
0
j t F( ) te dt
But
= (ax− 1 )+c a
e x e dx 2
ax ax
−ω − = − ω
ω =
−ω 1 2 0
j ( j t 1 ) j
e F( ) [( 1 j ) e 1 ]
(^1) j 2
−ω
t
f ‘(t)
1
0
- δ (t-1)
1
t
f ”(t)
δ (t)
- δ (t-1) - δ ’(t-1)
Find the Fourier transform of the waveform shown in Fig. 18.29.
Figure 18.
For Prob. 18.4.
′′=− δ + + δ′ + + δ − δ − − δ′ −
ω ω −ω −ω
(cos sin 1 )
2
ω+ω ω− ω
ω =
t 0
g’
2 δ(t+1)
–2δ(t–1)
t 0
4 δ(t)
g”
2 δ’(t+1)
–2δ(t–1)
–2δ(t+1)
–2δ’(t–1)
