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Signals and Systems by Smarajit Ghosh

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3.4 FOURIER TRANSFORMATION THEOREM

3.4.1 Linearity

If f1(t)image F1(ω) and f2(t)image F2(ω), it can be written that

 

F[a1f1(t) + a2f2(t)]image a1F1(ω) + a2F2(ω).

Proof:

 

image

3.4.2 Time Scaling

If a function f(t) is expanded in time domain, its Fourier transform compressed in frequency domain along ‘ω’ axis and the magnitude of |F(ω)| increases. Conversely, if a function ...

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