The impulse response of a second order FIR filter is:
h[n] = {-0.5, 2, -0.5}
Determine the filter outputs y[2] and y[7] for the following input signal:
x[n] = {2,4,6,4,2,4,2,4}
To calculate the filter output at a specific point, we must convolve the filter impulse response with the input signal up to that point.
For y[2]:
y[2] = h[0]*x[2] + h[1]*x[1] + h[2]*x[0]
y[2] = -0.5*6 + 2*4 - 0.5*2
y[2] = -3 + 8 - 1
y[2] = 4
For y[7]:
y[7] = h[0]*x[7] + h[1]*x[6] + h[2]*x[5]
y[7] = -0.5*4 + 2*2 - 0.5*4
y[7] = -2 + 4 - 2
y[7] = 0
Therefore, the filter output at y[2] is 4 and the filter output at y[7] is 0.