15
Aperiodic Signals
¥The Fourier transform of an aperiodic signal
can be found from integration of the time-domain waveform:
X( f ) has continuous variation in
both the
amplitude spectrum and the phase spectrum. Because each point in the amplitude spectrum of an Aperiodic
signal is infinitesimally higher in frequency than the last point, the voltage
at any point in the amplitude spectrum is infinitesimally small.
The
output of the Fourier transform is therefore not voltage, but the power spectral density of the waveform.
This value is the voltage of a single spectral line whose power equals
the amount of power contained an a 1 Hz wide frequency band with constant
spectral density.