Discrete-time signals

Discrete-timesignals

A discrete-time signal is a sequence or a series of signal values defined in

discrete points of time, see Figure 1. These discrete points of time can be

denoted tk where k is an integer time index. The distance in time between

each point of time is the time-step, which can be denoted h. Thus,

h = tk − tk−1 (1)

The time series can be written in various ways:

{x(tk)} = {x(kh)} = {x(k)} = x(0), x(1), x(2), . . . (2)

To make the notation simple, we can write the signal as x(tk) or x(k).

Examples of discrete-time signals are logged measurements, the input signal to and the output signal from a signal filter, the control signal to a physical

process controlled by a computer, and the simulated response for a dynamic

system.