September 2008
Beginner
834 pages
37h 13m
English
Content preview from Electric Circuits and Networks
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14.3 CONVERGENCE OF FOURIER TRANSFORMS
The Fourier transform of an aperiodic waveform v(t) is given by
It may be possible to evaluate this integral for a given v(t), but that does not make the integral the Fourier transform of v(t). It becomes the Fourier transform of v(t) only if v(t) can be constructed uniquely from V(jω) by means of the synthesis equation
Therefore, the integral in Eqn. 14.3-1 is the Fourier transform of v(t) only if the integral in Eqn. 14.3-2 converges to the value of v(t) for all t. If it does so, we assert that ...
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