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## Time-Domain Responses of Discrete-Time Model

This example shows how to obtain a step-response plot and step-response data for a discrete-time dynamic system model. Obtaining time-domain responses of discrete-time models is the same as for continuous-time models, except that the time sample points are limited by the sample time Ts of the model.

You can use the techniques of this example with commands such as impulse, initial, impulseplot, and initialpot to obtain time-domain responses of discrete-time models.

Create a discrete-time transfer function model and plot its response to a step input at $t$ = 0.

H = tf([-0.06,0.4],[1,-1.6,0.78],0.1);
step(H)

For discrete-time models, step plots the response at multiples of the sample time, assuming a hold between samples.

Compute the step response of H between 0.5 and 2.5 seconds.

[y,t] = step(H,0.5:0.1:2.5);

When you specify a time vector for the response of a discrete-time model, the time step must match the sample time Ts of the discrete-time model. The vector t contains the time points between 0.5 and 2.5 seconds, at multiples of the sample time of H, 0.1 s. The vector y contains the corresponding step response values.