Filter package

direct form 1 realization

  a[0] is assumed to be 1.0

start with the Z transform of a filter with transfer function H(z):

  Y(z) = H(z)·X(z)
  Y(z) = N(z)/D(z)·X(z)
  D(z)·Y(z) = N(z)·X(z)

Taking the inverse Z transform and collecting terms to one side gives:

  y[n] =   b[0]x[n]   + b[1]x[n-1] + ... + b[L]x[n-L]
         - a[1]y[n-1] - a[2]y[n-2] - ... - a[M]y[n-M]

               b0
  x[n] ----┬---|>-→(+)-------┬---→ y[n]
           ↓        ↑        ↓
          [z]  b1   |  -a1  [z]
           ├---|>-→(+)←-<|---┤
           ↓        ↑        ↓
          [z]  b2   |  -a2  [z]
           └---|>-→(+)←-<|---┘

BiQuad

BiQuad is a direct form I filter where the a and b polynomials are quadratic

b := [3]Float64{0.0045, 1.0, -0.0045} // numerator (filter zeros)
a := [3]Float64{1.0, -1.98, 0.991}    // denominator (filter poles)
y := BiQuad(b, a, x)

DirectForm1

DirectForm1 is a direct form I filter where the a and b polynomials are of any degree

b := []Float64{0.0045, 1.0, -0.0045} // numerator (filter zeros)
a := []Float64{1.0, -1.98, 0.991}    // denominator (filter poles)
y := DirectForm1(b, a, x)