Effect of Frequency Scaling:


The Inverse Fourier Transform of Y(w) = X(cw) is y(t) = |1/c| x(t/c). Therefore the time signal corresponding to the frequency scaled spectra

|Y(w)| = |X(cw)|

<Y(w) = <X(cw)

is

y(t) = |1/c| x(t/c)


Compare the magnitude spectrum of X(w) with the scaled magnitude spectrum of Y(w) = X(2w)

and the phase spectrum of X(w) with the scaled phase spectrum of Y(w) = X(2w)

to the corresponding time signals

x(t) = e-tu(t)
y(t) = (1/2)x(t/2) = (1/2)e-t/2u(t/2) = (1/2)e-t/2u(t)





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