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