Num contains the numerator and Den the denominator coefficients of the transfer function. The length of the Num and Den must be equal. If the numerator is of lower order that the denominator, then the numerator should be padded with zeros from the left. Transfer function:
Sum( b[k]*z^(-k) )
H(z) = ----------------------, from k = 0 to N-1.
Sum( a[k]*z^(-k) )
N = Num.Length = Den.Length.
b... Num vector
a... Den vector
H(z) is also written as:
Sum( b[k]*z^(-k) )
H(z) = ----------------------, k = 0.. N-1, m = 1..N-1
1 - Sum( a[m]*z^(-m) )
a[0] must always be 1.
IIR filters evaluate the difference equation:
y[i] = b[0]*x[i] + b[1]*x[i-1] + ... + b[N]*x[i-N]
+ a[1]*y[i-1] + ... + a[N]*y[i-N]
x[i] ... input sample
y[i] ... output (filtered) sample
References:
[1]Understanding digital signal processing, Richard G. Lyons, Prentice Hall, 2001.
