December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and Systems
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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:
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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