14.11 PARSEVAL'S RELATION FOR A FINITE-ENERGY WAVEFORM

Consider a signal v(t) which is of finite energy. All signals are—because we can not have infinite voltages or currents and because signals are switched on at some instant and switched off at another instant. We try to develop a relation between its normalised energy content En and its Fourier transform V(jω).

 

images

 

v(t) in a practical context is a real signal. Therefore, there is no error in expressing images

Substituting we get,

 

 

Reversing the order of integration,

 

 

This relationship ...

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