I came across the following problem in a signals graduate class:
Given the following general formula for a discrete causal filter, let's name (1):
$y[n] + \sum_{j=1}^{M} a_j*y[n-j] = \sum_{i=0}^{N} b_i*x[n-i]$
Find the vectors a,b of the above formula for the moving average which is given by the following formula, let's name (2):
$y[n] = \frac{1}{N+1} \sum_{i=0}^{N} x[n-i] $
We are given N, N=20.
Format of vectors a, b :
$a = [a_0,a_1,a_2,a_3,...,a_M]$
$b = [b_0, b_1, b_2, ..., b_N]$
What are the vectors a, b for the moving average filter?
One solution I thought was having all b's set to $\frac{1}{N+1}$ and a's equal to 0s. But is that the only solution?