1.2 M09 - an overview of discrete-time signals

[discrete-time signals]discrete-time signals

Although the discrete-time signal x(n) could be any ordered sequence of numbers, they are usually samples of a continuous-timesignal. In this case, the real or imaginary valued mathematical function x(n) of the integer n is not used as an analogy of aphysical signal, but as some representation of it (such as samples). In some cases, the term digital signal is usedinterchangeably with discrete-time signal, or the label digital signal may be use if the function is not real valued but takesvalues consistent with some hardware system.

Indeed, our very use of the term ``discrete-time" indicates the probable origin of the signals when, in fact, the independentvariable could be length or any other variable or simply an ordering index. The term ``digital" indicates the signal is probably going tobe created, processed, or stored using digital hardware. As in the continuous-time case, the Fourier transform will again be ourprimary tool.

Notation has been an important element in mathematics. In some cases, discrete-time signals are best denoted as a sequence ofvalues, in other cases, a vector is created with elements which are the sequence values. In still other cases, a polynomial is formedwith the sequence values as coefficients for a complex variable. The vector formulation allows the use of linear algebra and thepolynomial formulation allows the use of complex variable theory.