Checking Linearity and Shift Invariance: Step-by-Step Guide

[hanafnaf]

please help me in this problem

Homework Statement

how make check the linearity and shift invarient for the system

I want to determine whether the system is linear and shift invarientby steps

g(m,n) = f(m,-1) + f(m,0) + f(m,1)

g(x) = (integration from +infinety to - infinety) f(x,z) dz

please help me
Thanks a lot

Homework Equations

The Attempt at a Solution

 

[Com3t]

Add a variable for what you want to show is invariant.
Show that it makes no difference in the equation.

For instance, derivative of a function is invariant with respect to a constant added.
So you make the constant an independent variable. Take a derivative. Notice that the derivative of the independent variable goes to zero...