Digital Signal Processing Dynamic Systems - Digital Signal Processing

What are the Dynamic Systems in Digital Signal Processing?

When a system depends on the past and future value of the signal at any instant of the time then it is called as dynamic system. In contrast to static systems, these are not memory less systems as they will store past and future values and they require some memory. Let us get an understanding on this theory through some examples.

Examples

Let’s find out if the following systems are dynamic.

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In this case if we put t = 1 in the equation, it will be converted to x(2), which is a future dependent value. As we are giving input as 1, it is showing value for x(2). As it is a future dependent signal, so clearly it is a dynamic system.

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In this case, whatever value we will put, it will show that time real value signal. It will not have any dependency on future or past values. So, it is not a dynamic system rather it is a static system.

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Here, if we substitute t = 1, one signal will show x(1) and another will show x(-1) which is a past value. In the same way, if we will put t = -1 then one signal will show x(-1) and another will show x(1) which is a future value. So, clearly it is a case of Dynamic system.

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In this case, as the system is cosine function, it will have a specific domain of values which lie between -1 to +1. So, whatever values we will put, result will be within the specified limit. Therefore, it is a static system

From the above examples, it can be concluded that

  • All time shifting cases signals are dynamic signals.
  • In case of time scaling too, all signals are dynamic signals.
  • Integration cases signals are dynamic signals.

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