Final Answer:
The discrete-time convolution sum y[n] = (-1)^n * 2^n * u[-n+2] is: y[n] = { ... 0, 0, 0, 0, -2u[0], 2u[1], -4u[2], 4u[3], ... }
Step-by-step explanation:
The discrete-time convolution sum y[n] = (-1)^n * 2^n * u[-n+2] can be determined using the following steps:
Shift the sequence u[n] two positions to the right:
u[-n+2] = { ... 0, 0, u[0], u[1], u[2], u[3], ... }
Multiply the shifted sequence u[-n+2] by the sequence (-1)^n * 2^n:
y[n] = (-1)^n * 2^n * u[-n+2] = { ... 0, 0, 0, 0, -2u[0], 2u[1], -4u[2], 4u[3], ... }
Simplify the expression:
y[n] = { ... 0, 0, 0, 0, -2u[0], 2u[1], -4u[2], 4u[3], ... }
Therefore, the discrete-time convolution sum y[n] = (-1)^n * 2^n * u[-n+2] is:
y[n] = { ... 0, 0, 0, 0, -2u[0], 2u[1], -4u[2], 4u[3], ... }