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Signals and Systems by Smarajit Ghosh

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3.5 FOURIER TRANSFORM OF PERIODIC SIGNALS

The periodic functions like sine wave, triangular wave and saw tooth wave etc. exist for t = − ∞ to t = ∞ are truly periodic. A perpetual periodic function has infinite area under the rectified condition and therefore this does not satisfy the absolute integrability condition. Hence direct use of Fourier transform gives an inaccurate result.

To find the Fourier transform any of the following two approaches must be taken into account:

  • We use Fourier transforms after making use of the exponential Fourier series of the function.
  • The Fourier transform of the periodic function is found out for a limited period of time say ‘τ’ and let τ tends to infinity. Now we can obtain Fourier transform of the perpetual ...

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