The Fourier transforms of cosine and sine functions are shown in Fig. 14.7-1.
593
14.8 FOURIER TRANSFORMS OF SOME SEMI-INFINITE DURATION WAVEFORMS
Re(V(j ))
cos
1
1
–1
–1
t
ω
Im(V(j ))
ω
ω
ππ
π
π
ω
ω
π
–
–
–
0
ω
0
t
ω
0
sin
t
ω
0
t
ω
0
ω
0
ω
0
–
ω
0
2
π
π
2
π
2
π
π
–
–
π
2
π
Fig. 14.7-1 Fourier transforms of Unit Cosine and Unit Sine Waveforms
14.8 FOURIER TRANSFORMS OF SOME SEMI-INFINITE DURATION
WAVEFORMS
Inputs, even if they are periodic waveforms, are switched on to the circuit at some finite
time-instant. This fact is usually brought out by specifying an input function as f(t) u(t), where
f(t) is a periodic or aperiodic waveform. A DC voltage of V applied to the circuit from t ⫽0
is specified as ...
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