Effect of Amplitude Scaling:
The Fourier transform
of y(t) = ax(t) is Y(w) = aX(w) .
Therefore the magnitude spectrum of
y(t) is given by
|Y(w)| = |a| |X(w)|
The phase spectrum of y(t) is given by
<Y(w) = <X(w),
if a > 0
<Y(w) = p + <X(w),
if a <0
Compare the two exponential signals
x(t) = e-tu(t)
y(t) = 3 x(t) = 3 e-tu(t)
with the corresponding magnitude spectra
and phase spectra
and also the two exponential signals
x(t) = e-tu(t)
y(t) = -3 x(t) = -3 e-tu(t)
with the corresponding magnitude spectra
and phase spectra
return to Magnitude and Phase Spectra page