Consider the signal (a) Show that any sequence x(n) can be decomposed as and...

Consider the signal

(a) Show that any sequence x(n) can be decomposed as

and express c_k in terms of x(n).

(b) Use the properties of linearity and time invariance to express the output y(n) = in terms of the input x(n) and the signal is an LTT system.

(c) Express the impulse response in terms of g (n)