Determine output y[7] for the following moving average filter and input sequence x[n]:

Question

y[n] = 0.25x[n] + 0.25x[n – 1] + 0.25x[n – 2] + 0.25x[n – 3]
x[n] = {1, 2, 6, 3, 1, 3, 4, 4, 2}

Answer 1

To find the value of y[7], we first need to determine the values of x[n-1], x[n-2], and x[n-3] using the given input sequence x[n].

x[n-1] = x[6] = 4
x[n-2] = x[5] = 3
x[n-3] = x[4] = 1

Now we can substitute these values into the moving average filter equation to find y[7]:

y[7] = 0.25*x[7] + 0.25*x[6] + 0.25*x[5] + 0.25*x[4]
y[7] = 0.25*2 + 0.25*4 + 0.25*3 + 0.25*1
y[7] = 0.5 + 1 + 0.75 + 0.25
y[7] = 2.5

Therefore, the output y[7] for the given moving average filter and input sequence is 2.5.