Final answer:
To find the output transform when the input is given as x[n] = δ[n+3] + δ[n+2] + δ[n] + δ[n] + δ[n-3] with an impulse response h[n] = 5δ[n], we can use the convolution property of the system. The output transform is given by the convolution of the input transform and the impulse response. The correct option is D) 5e^(j2ω) + 5 + 5e^(-j3ω) + 5.
Step-by-step explanation:
To find the output transform when the input is given as x[n] = δ[n+3] + δ[n+2] + δ[n] + δ[n] + δ[n-3] with an impulse response h[n] = 5δ[n], we can use the convolution property of the system. The output transform is given by the convolution of the input transform and the impulse response:
y[n] = x[n] * h[n]
Using the given values of x[n] and h[n], we can compute the convolution:
y[n] = (δ[n+3] + δ[n+2] + δ[n] + δ[n] + δ[n-3]) * 5δ[n]
Expanding the convolution and simplifying, we get:
y[n] = 5δ[n+3] + 5δ[n+2] + 10δ[n] + 5δ[n-3]
Therefore, the correct option is D) 5e^(j2ω) + 5 + 5e^(-j3ω) + 5.