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