## 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^{-t}u(t)

y(t) = 3 x(t) = 3 e^{-t}u(t)

with the corresponding magnitude spectra

and phase spectra

and also the two exponential signals

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

y(t) = -3 x(t) = -3 e^{-t}u(t)

with the corresponding magnitude spectra

and phase spectra

return to Magnitude and Phase Spectra page