1. For FIR filter having the specified impulse response h[n] determine the specified output y[n] for

Question

a given input sequence x[n]. Show your work.

h[n] = {-1, 2, -1}
x[n] = {2, 6, 7, 3, 4, 1}

y [?] =?

Answer 1

To find the output sequence y[n], we need to convolve the input sequence x[n] with the impulse response h[n].

Given:
h[n] = {-1, 2, -1}
x[n] = {2, 6, 7, 3, 4, 1}

To find y[n], we need to perform the following convolution:

y[n] = x[n] * h[n] = Σ x[k] * h[n-k]

For n = 0:
y[0] = 2*(-1) + 6*2 + 7*(-1) = -2 + 12 - 7 = 3

For n = 1:
y[1] = 6*(-1) + 7*2 + 3*(-1) = -6 + 14 - 3 = 5

For n = 2:
y[2] = 7*(-1) + 3*2 + 4*(-1) = -7 + 6 - 4 = -5

For n = 3:
y[3] = 3*(-1) + 4*2 + 1*(-1) = -3 + 8 - 1 = 4

Therefore, the output sequence y[n] is:
y[n] = {3, 5, -5, 4}