For a digital FIR filter with the following impulse response h[n] determine the specified output value y[n] for given input sequence x[n]. show your work.

Question

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

y[4] =

Answer 1

To find y[4], we need to convolve the input sequence with the impulse response:

y[n] = x[n] * h[n]

y[4] = x[4] * h[0] + x[3] * h[1] + x[2] * h[2] + x[1] * h[3] + x[0] * h[4]

y[4] = (-1) * 1 + 1 * 3 + (-2) * 1 + 1 * (-1) + 1 * (-1)

y[4] = -1

Therefore, the specified output value y[4] for the given input sequence x[n] is -1.