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-tu(t)
y(t) = x(4t) = e-4tu(4t) = e-4tu(t)
with the corresponding magnitude spectra
and phase spectra
and also the two exponential signals
x(t) = e-tu(t)
y(t) = x(-4t) = e4tu(-4t) = e4tu(-t)
with the corresponding magnitude spectra
and phase spectra
return to Magnitude and Phase Spectra page