*Signal:
A system process input signals to produce output signals. For example, a CD player takes signals on CD and transforms them into a signal and send them to the loudspeaker. A communication system consisting of a transmitter, channel and receiver is also an example of the system.
Mathematically,
Y(t)/X(t).
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| Figure: Signals and Systems |
* Following are the Types of Systems:
- A static system is memoryless. It has no storage device.
- A dynamic system process memory. It has storage devices.
- Here static refers to the condition if present output depends only on present input.
- While dynamic depicts when the present output depends on past or future input.
2. Causal , non causal and anticausal system-
- If present output depends upon present or present + past inputs.
* Noncausal :
- When present output depends upon present + future or present + past + future or past + future inputs.
- A special case of non-causal is anti causal which shows if the present output depends only on future inputs.
Note: that static systems are always causal. Remember that if the impulse response is only representing positive values then it is a causal system. For positive and negative values it is non-causal and if there are only negative values then it is an anti causal system.
3. Time-Variant and Time-Invariant systems-
* Invariant:
If a time shift in the input results in identical time shapes in outputs without changing the nature of output then it is termed as an invariant system. And vice versa for Time-Variant systems.
Conditions for a system to be Time-invariant:
1. They must not be any scaling in x(t) or y(t).
2. Coefficients must not be a function of time.
3. Any extra term except Xt and Yt must be zero or any constant.
4. Linear and nonlinear systems:
The Linear system satisfies the superposition principle that is it follows both the homogeneity phenomena as well as the additivity criteria.
There are certain conditions for a system to be linear:
1. graph between output and input must be throughout a straight line passing through origin without having saturation or dead time.
2. If a system is represented by a differential equation then the equation must be linear.
3. System must follow zero input zero output criteria.
5. Invertible and Non-Invertible system:
A system is said to be invertible if the system produces distinct input for distinct output.
If the input can be determined by observing the output.
It is possible to design an inverse system such that if the inverse system is cascaded with the original system then the output of the overall system will be the input itself.
6. Stable and unstable system:
The system is said to be bounded input bounded output stable (BIBO stable) if every bounded input results in the bounded output.
Note: The mathematical representation of all the Types Of Systems is available in the PDF given below so that you can have it in your hand at ease. Please find attached.
👉👉To download handwritten notes for 👈👈
👉👉Types of system.👈👈
To be continued...
In our next article, we'll discuss Linear Time-Invariant Systems.
You can also check out our last article about Signals and Systems here
👉👉Transformation in Independent variable of signals👈👈 .
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Reviewed by Oyetechy.com
on
March 19, 2021
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