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