Hello Roger,
First I suppose the length N, is the output vector length. Right? Let's say your initial index is 1. Thus, samples before x[1] (i.e., x[0] x[-1] ... x[1-M]) can be simply considered 0 (or, if you prefer, they could be passed as an argument of the function). Then, the first sample of the vector x can be computed as,
x[1]=v[1];
At the next step, you can use x[1] since you just computed its value. So,
x[2]=a[1]*x[1]+v[2];
Then,
x[3]=a[1]*x[2]+a[2]*x[1]+v[3];
And so on and so forth. Of course, you'll need to implement these steps programmatically.
