Static & Dynamic Systems | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

Some systems have feedback and some do not. Those, which do not have feedback systems, their output depends only upon the present values of the input. Past value of the data is not present at that time. These types of systems are known as static systems. It does not depend upon future values too.

Since these systems do not have any past record, so they do not have any memory also. Therefore, we say all static systems are memory-less systems. Let us take an example to understand this concept much better.

Example

Let us verify whether the following systems are static systems or not.

  • y(t) = x(t) + x(t − 1)
  • y(t) = x(2t)
  • y(t) = x = sin[x(t)]

a) y(t) = x(t) + x(t − 1)

Here, x(t) is the present value. It has no relation with the past values of the time. So, it is a static system. However, in case of x(t-1), if we put t = 0, it will reduce to x(-1) which is a past value dependent. So, it is not static. Therefore here y(t) is not a static system.

b) y(t) = x(2t)

If we substitute t = 2, the result will be y(t) = x(4). Again, it is future value dependent. So, it is also not a static system.

c) y(t) = x = sin[x(t)]

In this expression, we are dealing with sine function. The range of sine function lies within -1 to +1. So, whatever the values we substitute for x(t), we will get in between -1 to +1. Therefore, we can say it is not dependent upon any past or future values. Hence, it is a static system.

From the above examples, we can draw the following conclusions −

  • Any system having time shifting is not static.
  • Any system having amplitude shifting is also not static.
  • Integration and differentiation cases are also not static.

If a system depends upon the past and future value of the signal at any instant of the time then it is known as dynamic system. Unlike static systems, these are not memory less systems. They store past and future values. Therefore, they require some memory. Let us understand this theory better through some examples.

Examples

Find out whether the following systems are dynamic.

a) y(t) = x(t+1)

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

b) y(t) = Real[x(t)]

Static & Dynamic Systems | Digital Signal Processing - Electronics and Communication Engineering (ECE)

In this case, whatever the value we will put it will show that time real value signal. It has no dependency on future or past values. Therefore, it is not a dynamic system rather it is a static system.

c) y(t) = Even[x(t)]

Static & Dynamic Systems | Digital Signal Processing - Electronics and Communication Engineering (ECE)

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

d) y(t) = cos[x(t)]

In this case, as the system is cosine function it has a certain domain of values which lies between -1 to +1. Therefore, whatever values we will put we will get the result within specified limit. Therefore, it is a static system

From the above examples, we can draw the following conclusions −

  • 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.
The document Static & Dynamic Systems | Digital Signal Processing - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Digital Signal Processing.
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FAQs on Static & Dynamic Systems - Digital Signal Processing - Electronics and Communication Engineering (ECE)

1. What is the difference between static and dynamic systems in electrical engineering?
Static systems in electrical engineering refer to systems that do not change with time, where the output is solely dependent on the current input. On the other hand, dynamic systems are time-varying and the output not only depends on the current input but also on the previous inputs and the system's internal state.
2. What are some examples of static systems in electrical engineering?
Some examples of static systems in electrical engineering include resistors, capacitors, and inductors. These components do not change their behavior with time and their output is solely determined by the current input.
3. Can you provide examples of dynamic systems in electrical engineering?
Certainly! Examples of dynamic systems in electrical engineering include circuits with energy storage elements such as capacitors and inductors. These systems exhibit time-varying behavior and their output depends not just on the current input but also on the history of inputs and the system's internal state.
4. How do static and dynamic systems differ in terms of stability?
Static systems are inherently stable as they do not change with time. On the other hand, dynamic systems can exhibit stability or instability based on their behavior. Stability in dynamic systems refers to the output of the system remaining bounded in response to a bounded input. Unstable dynamic systems can lead to oscillations or exponentially growing outputs.
5. Are there any practical applications where both static and dynamic systems are used together?
Yes, many practical applications in electrical engineering utilize both static and dynamic systems together. One common example is in power systems, where static components like transformers and transmission lines are used alongside dynamic systems such as generators and control systems to ensure stable and efficient power distribution.
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