Effect of Time Shifting:


The Fourier transform of y(t) = x(t - to) is Y(w) = e- jwto X(w) . Therefore the magnitude spectrum of y(t) is given by

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

The phase spectrum of y(t) is given by

<Y(w) = -wto + <X(w)

(Be careful not to mix radians and degrees!)


Compare the two exponential signals

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

with the corresponding magnitude spectra

and phase spectra





return to Magnitude and Phase Spectra page