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Signals and Systems by Smarajit Ghosh

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3.2 CONDITION FOR THE EXISTENCE OF FOURIER INTEGRAL

The sufficient condition for the existence of Fourier transform of a function f (t) is that the area under the function f (t) be finite. Hence, for the existence of Fourier transform the following relation must be satisfied:

 

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The above absolute integrability criteria must be satisfied to give the guarantee for the existence of Fourier transforms. The direct substitution of f(t) in the Fourier integral may give absurd result for the functions for which the above condition is not satisfied.

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