Hi guys, I need help with finding of impulse response of the following sequence:

y(n) = x[n] + c

my answer by substituting x[n] with delta x
h(k) = delta (x) + c

correct?

 

correct?

I don't think so. The question looks very simple and your answer looks logical. But if you try to use a simple input say unit step(x(n)=u(n)) the two answers differ(the one got through convolution and one by direct substitution).
The reason behind this is that unit impulse rule is only applicable for LTI(linear and time-invarient) systems.
But yours is not linear(its only incrementally linear).
In simple words a thing called impulse response(like transfer function) does not exist for your system.

But that said you can just say that your answer will be the output of the system if the input is an impulse.

 

@narasimhan

Thank you, this confirms my observation that I cannot obtain the H(z) using z-transform. Now I have to show it is non-linear or time-variant. Tricky Professor.

Is this in line with what the rest think?

 

Is this in line with what the rest think?

Its time invariant but certainly non-linear.
let x1(n) =1 then output y1(n)=1+c
let x2(n) =2 then output y2(n)=2+c

let x(3)=x1(n)+x2(n)=3 then y3(n)=3+c
but y1(n)+y2(n)=3+2c which is not equal to y3(n) hence its non-linear.

 

Its time invariant but certainly non-linear.
let x1(n) =1 then output y1(n)=1+c
let x2(n) =2 then output y2(n)=2+c

let x(3)=x1(n)+x2(n)=3 then y3(n)=3+c
but y1(n)+y2(n)=3+2c which is not equal to y3(n) hence its non-linear.

Thank you for the clear steps shown (missed out on scaling property though nevertheless proves the point it is non-linear)

Is it true that a non-linear system do not have an impulse response? Or does this belong to more advance topics (nonlinear impulse response)

 

missed out on scaling property

It was not missed. It was intentionally left out. Its only needed if you can't prove non-linearity via the simple additive property.

nonlinear impulse response

There is nothing called nonlinear impulse response. I think it requires state diagram analysis.