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 ...
Get Electric Circuits and Networks now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
