Analyzing Time-Series Models

A time-series model has no inputs. However, you can use many response computation commands on such models. The software treats (implicitly) the noise source e(t) as a measured input. Thus, step(sys) plots the step response assuming that the step input was applied to the noise channel e(t).

To avoid ambiguity in how the software treats a time-series model, you can transform it explicitly into an input-output model using noise2meas. This command causes the noise input e(t) to be treated as a measured input and transforms the linear time series model with Ny outputs into an input-output model with Ny outputs and Ny inputs. You can use the resulting model with commands, such as, bode, nyquist, and iopzmap to study the characteristics of the H transfer function. For example:

iosys = noise2meas(sys);
% step response of H if the step command was applied 
% to the noise source e(t)
step(iosys) 
% poles and zeros of H
iopzmap(iosys) 

You can calculate and plot the time-series spectrum directly (without conversion using noise2meas) using spectrum. For example:

spectrum(sys)  

plots the time-series spectrum amplitude:

Φ(ω)=H(ω)2

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