¥Analog and digital signals in the time and the frequency
¥
domain.
¥The time domain is simply the signal level
expressed as a function of time.
¥The frequency domain is comprised of amplitude
and a phase for an infinite number of cosine functions. These correspond to the superposition of an infinite number of sinusoidal waveforms in
the time domain.
¥To convert from the time domain to the
frequency domain, we take the Fourier transform of the time
domain representation.
¥The frequency
domain representation of a signal does not change with time, but the Fourier
transform for the signal over an infinitely long time period would be
impossible. Instead, we assume
that the signal has some finite duration, over a sampling interval:
¥1. We assume
that outside of the sampling interval, the signal repeats itself, so that the
signal is periodic.
¥2. An
alternative assumption is that the time-domain signal has a zero value outside
of the sampling interval, so that the signal is aperiodic.