Shift Invariant and Shift Variant DTS

[Eshal]

Hello to all experts.

I understand how to check the DTS for shift variant and shift invariant.

But I am confused with this example:
Check for shift invariance for the below system.

y = x(-n)

Attempted solution:

shift the input by k samples gives
y(n,k) = x(-n-k)

now shifting the output by k samples gives
y(n-k) = x(-n-k)
Hence y(n,k) = y(n-k)
So it is Shift Invariant system.

But book examples says something different that the given system is Shift Variant. See the image below of the book's example:


How does 1.8.11 and 1.8.12 come? I don't understand these equations.

Thank you ^_^

 

[zorro]

Hi Eshal,

I think that it will be more apparent considering the more general case y=x(C*n) .
In the example you have C=-1, but please consider instead C=2.
Take an arbitrary waveform for x, for instance a box lasting 3 samples starting at n=0.
Plot x, y, x(n-k), y(n,k) and y(n-k) for k=4.
I hope this will help.

Z

 

[Eshal]

:-?

sorry.