Electronics and Communication Engineering - Signals and Systems

F.T. of conjugate symmetric function is always real.

For time invariant system

y(n, k) = y(n - k), where y(n, k) mean shift the input by n - k, while y(n - k) mean change all the n

(a) y[n] = x[2n]

⇒ y(n, k) = x[2n - k]

y(n - k) = x[2(n - k)]

y(n, k) ≠ y(n - k) Time variant

(b) y[n] = x[n] x[n - 1]

y[n, k] = x[n - k] x[n - k - 1]

y[n - k] = x[n - k] x[n - k - 1]

y[n, k] = x[n - k] Time Invariant

(c) y[n] = x[n/2] ⇒ y[n, k]

⇒ y[n - k]

y[n, k] ≠ y[n - k] Time variant.

I =(2² + 6² + 24)^0.5 = 64 = 8.

and E.S.D. of g(t) = |G(f)|²

So E.S.D. of G_T(t) = |G(f)|² .

Use power series method to solve it.