Well guys, this is the third notes about Linear Signal and System. The notes will gives you a brief explanation and description about System.
Some of the topics covered in this notes are :
1. Brief explanation and definition of System
2. Properties of System including Homogeinity, Additivity, Time Invariance, and Invertibility
3. Explanation about Linear System, some properties of Linear System including
Stability,Causality, Incremental Linearity, and Static/Dynamic System.
4. A brief explanation about Non-Linear System
5. A brief explanation about Feedback System
6. How to perform System type checking(How to check whether a system is linear or non-linear,
time invariant or time variant, causal and non-causal.
I also will provide an e-book Schaum's Outline About Signal and System. This e-book contains some of good exercise and simple explanation that will help you to understand the concept of Linear Signal and System. Some of the exercises in the previous notes were also taken from this e-book.
Maybe I will list some of key points in this note :
- A system has excitation(input) and response(output)
- A system has some properties :
1. Homogeinity : multiplying an input by a constant simply result in multiplied output by that
constant too.
2. Additivity : summing some input simply will cause a response that is the sum of the
response of each input.
3. Time Invariance : delaying an input to a system simply will cause a delayed ouput from the
system
4. Invertibility : unique input for a unique response
- A linear system is a system that is both homogenous and additive.
- A Linear Time Invariant System is a linear system that is Time Invariant
- A system said to be stable if the system has BIBO(Bounded Input and Bounded Output)
- A system said to be Causal if the system's response doesn't depend on input from the future
time, the system's response at a time only depends from the input up to that time.
- Incremental Linearity means a Linear System that have initial condition as an offset added to
the response.
- Static System is a system said to have no memory. The response at a time only depends on
arbitrary excitation at that time
- Dynamic System is a system said to have memory. The response at a time also depends on
excitations at another time.
- Non-Linear System is a system whose the relationship of the amplitude of excitation and
response are not linear. An example of Non-Linear System is a product of 2 system(using
Analog Multiplier)
- Feedback System is a system whose have an output at a time that will act as another input
beside the excitation at another time/state.
- Linearity check use the Homogeinity and Additivity properties :
u(t) = a . x(t) + b . y(t)
- Time Invariant check use the unit advance properties :
x[n + 1] = q . x[n]
Well that's some of key point that I think were important. You can just download the notes from the link belown for more specific explanation and solution, and also the ebook Schaum's Outline of Linear Signal and System :
Description and Analysis of System(4shared.com)
Schaum's Outline of Linear Signal and System Ebook(4shared.com)
Well sorry for the late post, hope you all get benefit from it.
Best Regards,
Admin
Some of the topics covered in this notes are :
1. Brief explanation and definition of System
2. Properties of System including Homogeinity, Additivity, Time Invariance, and Invertibility
3. Explanation about Linear System, some properties of Linear System including
Stability,Causality, Incremental Linearity, and Static/Dynamic System.
4. A brief explanation about Non-Linear System
5. A brief explanation about Feedback System
6. How to perform System type checking(How to check whether a system is linear or non-linear,
time invariant or time variant, causal and non-causal.
I also will provide an e-book Schaum's Outline About Signal and System. This e-book contains some of good exercise and simple explanation that will help you to understand the concept of Linear Signal and System. Some of the exercises in the previous notes were also taken from this e-book.
Maybe I will list some of key points in this note :
- A system has excitation(input) and response(output)
- A system has some properties :
1. Homogeinity : multiplying an input by a constant simply result in multiplied output by that
constant too.
2. Additivity : summing some input simply will cause a response that is the sum of the
response of each input.
3. Time Invariance : delaying an input to a system simply will cause a delayed ouput from the
system
4. Invertibility : unique input for a unique response
- A linear system is a system that is both homogenous and additive.
- A Linear Time Invariant System is a linear system that is Time Invariant
- A system said to be stable if the system has BIBO(Bounded Input and Bounded Output)
- A system said to be Causal if the system's response doesn't depend on input from the future
time, the system's response at a time only depends from the input up to that time.
- Incremental Linearity means a Linear System that have initial condition as an offset added to
the response.
- Static System is a system said to have no memory. The response at a time only depends on
arbitrary excitation at that time
- Dynamic System is a system said to have memory. The response at a time also depends on
excitations at another time.
- Non-Linear System is a system whose the relationship of the amplitude of excitation and
response are not linear. An example of Non-Linear System is a product of 2 system(using
Analog Multiplier)
- Feedback System is a system whose have an output at a time that will act as another input
beside the excitation at another time/state.
- Linearity check use the Homogeinity and Additivity properties :
u(t) = a . x(t) + b . y(t)
- Time Invariant check use the unit advance properties :
x[n + 1] = q . x[n]
Well that's some of key point that I think were important. You can just download the notes from the link belown for more specific explanation and solution, and also the ebook Schaum's Outline of Linear Signal and System :
Description and Analysis of System(4shared.com)
Schaum's Outline of Linear Signal and System Ebook(4shared.com)
Well sorry for the late post, hope you all get benefit from it.
Best Regards,
Admin
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