14.3 CONVERGENCE OF FOURIER TRANSFORMS

The Fourier transform of an aperiodic waveform v(t) is given by

 

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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

 

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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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