Time Waveform

In digital signal processing, a signal's time-waveform is usually a real-valued function of an integer sample number, corresponding to continuous amplitude versus discrete time. This means that, at any sampling instant $nT$, the amplitude may take on any real value. The time-waveform may be pictured as a bar graph that extends forever to the left and right.

By convention, a filter input signal is usually denoted by $x(n)$, giving the signal's amplitude at time sample $n$. Similarly, a filter output is usually called $y(n)$. In both cases, $n$ is an integer, while $x(n)$ and $y(n)$ are usually real numbers. This notation should be comfortable for anyone who has written a computer subroutine for processing samples of digitized sound.