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Why do we use a step signal most frequently as a test signal in signal processing and control systems? What is the reason for not (frequently) using other signals? Especially in MATLAB and Simulink

For an example scenario, see the Simulink model in the attached snap where we are trying to implement and observe the series combination of two systems:

enter image description here

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  • \$\begingroup\$ A step signal contains all frequencies (at least in theory) and is easy to generate. A step is a simple expression using the s-transformation. \$\endgroup\$
    – Uwe
    Commented Sep 26, 2022 at 7:43
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    \$\begingroup\$ Engr <-- what's the alternative to a step signal? What do you suggest? \$\endgroup\$
    – Andy aka
    Commented Sep 26, 2022 at 8:41

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It is an useful test signal to see what the time domain response of the system is, if you are interested in the parameters it can tell you. It tells you how fast the system reacts to it, is there overshoot, is there ringing, how much is the settling time to certain error band, etc.

So whatever the system is, sometimes the user input is a step. For example, a step input might be a command to seek hard drive heads from track 0 to track 1000, and see how the head actually moves.

Other waveforms are useful too, they just don't give you the time domain step response, they are useful in other ways.

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The characteristic properties of a system (very often with negative feedback) can be analyzed and described in the (a) frequency domain or (b) time domain. In this context, it is important to know that both domains are interrelated by the Laplace-transformation.

Example: The timely response of a system to a step input (the "step response" g(t)) can be found when the inverse Laplace transformation is applied to H(s)/s (H(s) is the transfer function of the system).

As an example, for a second order system the form of the step response contains information about the pole location in the complex frequency plane (pole frequency, natural freqency, damping factor, stability parameters).

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