## Effect of Time Shifting:

The Fourier transform
of y(t) = x(t - t_{o})
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) = -wt_{o} + <X(w)
(Be careful not to mix radians and degrees!)

Compare the two exponential signals

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