TABLE OF CONTENTS A discrete-time system is implemented as a set of difference equations. A difference equation is a recursive algebraic equation that computes the next value of a discrete output given the current and previous values of the equation input, output, and state variables. Updates to a discrete-time system occur at equally spaced points in time. Each update involves evaluation of the equations to compute the new values of the states and the outputs.
In a general discrete-time system, the output at any time is a function of the current system input, the input at previous time steps, and previous output values. As with continuous-time systems described by differential equations, difference equations can be linear or nonlinear and time invariant or time varying.
An example linear difference equation appears in Eq. 8.1. This equation represents the continuous-time transfer function Y/ X = 1/( s 2 + 2 s + 1) after conversion to discrete time by use of the zero-order hold method and with a sampling interval of 0.1 seconds. The zero-order hold and other discretization methods will be discussed in the next section. I discuss the selection of appropriate discrete system step times in Section 8.5.
| (8.1) |  |
The subscripts in Eq. 8.1 represent the sample number in the discrete system's input and output sequences as follows.
x n is the current input value.
x n -1 is the input value from the previous time step.
y n +1 is the...
