Part a

The system is NOT time-invariant

The general formulas for te system are:

x[n] = d[n-k]

y[n] = (k+1)^2 * d[n-(k+1)]

Shifting by a constant means that

x[n-a] = d[n-k-a]

y[n-a] = (k+1)^2 * d[n-(k+1)-a]

As seen from this procedure, when shifted the y[n-a] has a multiplying (k+1)^2 that does not yield the same value as in the nonshifted equation.

Part b

The input X[n] = u[n] will yield y[n] = u[n-1] because the system is linear.

Alumni Liaison

Questions/answers with a recent ECE grad

Ryne Rayburn