linear system - show that the system is not linear

[bleach118]

linear system

i am studying the linear system in DSP, but hardly i can understand it. how i answer the questions when i am asked determine whether the system is linear or not linear.

is there a rule i can depend on making my answers.

take for example y[n] =2x[n] +3
show that the system is not linear


best regard

 

[m_pourfathi]

Re: linear system

There are three criterias to determine the linearity of a system:
(assuming y is the output and x is the input)


1- if y = f(x) then a*y = f(a*x)

2- if y1 = f(x1) and y2 = f(x2) then y1 + y2 = f(x1 + x2)

3- if x = 0 then y=f(0) = 0

If a system can satisfy the criterias above, it is linear, but sometimes, proving such thing needs creativity.
So to answer to your question I have to say there is a rule but checking the rule might not be so straight forward sometimes.

 

[bleach118]

Re: linear system

There are three criterias to determine the linearity of a system:
(assuming y is the output and x is the input)


1- if y = f(x) then a*y = f(a*x)

2- if y1 = f(x1) and y2 = f(x2) then y1 + y2 = f(x1 + x2)

3- if x = 0 then y=f(0) = 0

If a system can satisfy the criterias above, it is linear, but sometimes, proving such thing needs creativity.
So to answer to your question I have to say there is a rule but checking the rule might not be so straight forward sometimes.

that was helpfull thank you

so all what i need to do is to know which parts of the 3 part i need to implement depending on what formula i am having.

this not easy, i mean no golden rule or any way in which it can be more easy..

BEST REGARD

 

[kataria0]

Re: linear system

i am studying the linear system in DSP, but hardly i can understand it. how i answer the questions when i am asked determine whether the system is linear or not linear.

is there a rule i can depend on making my answers.

take for example y[n] =2x[n] +3
show that the system is not linear


best regard

Strictly speaking y[n]=2x[n]+3 is "incrementally linear" because of the offset of 3.
Incrementally linear because delta y/delta x= constant=2 in this case.
But in engineering society incrementally linear systems are also considered linear.

 

[LvW]

Re: linear system

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But in engineering society incrementally linear systems are also considered linear.

Are you really speaking for the whole "engineering society" ?
I never have heard about such an agreement. I wonder where your information comes from.

 

[bleach118]

Re: linear system

thanks but can you make it easy for me please

 

[xulfee]

linear system

just check super position principle,suppose y[n]=F[x],u r getting output y1 for input x1,y2 for x2,now consider x3=x1+x2 is input now if ur output y3=y1+y2 then ur system is linear otherwise not,u can also use homogenity

 

[Kral]

Re: linear system

bleach118,
If you are not concerned with the difference between linear and incrementally linear, then an easy way to test the function is to move all constant terms to the left side of the equation and use a change of variable. In your case the equation becomes z = y[n]-3 = 2x[n]. The new equation (for z) passes test number 2 as described by m_pourfathi.
.
I agree, for the most part, with Lvw regarding linearity. In most cases the main concern over linearity is whether the system distorts the input. In your example, the output is a faithful scaled reproduction of the input except for a fixed offset in the output.
Regards,
Kral