Signals and Systems

3.4 FOURIER TRANSFORMATION THEOREM

3.4.1 Linearity

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

 

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

Proof:

 

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 ...