## Effect of Time Scaling:

The Fourier transform of y(t) =x(bt) is Y(w) = |1/b| X(w/b).
Therefore the magnitude spectrum of y(t) is given by

|Y(w)| = |1/b||X(w/b)|
The phase spectrum of y(t) is given by

<Y(w) = <X(w/b)

Compare the two exponential signals

x(t) = e^{-t}u(t)

y(t) = x(4t) = e^{-4t}u(4t) = e^{-4t}u(t)

with the corresponding magnitude spectra

and phase spectra

and also the two exponential signals

x(t) = e^{-t}u(t)

y(t) = x(-4t) = e^{4t}u(-4t) = e^{4t}u(-t)

with the corresponding magnitude spectra

and phase spectra

return to Magnitude and Phase Spectra page