// Although b0 is not a used coefficient, space for it is still expected
func parallelizeFilterStages(stageAs1, stageBs1, stageAs2, stageBs2 []float64) (stageAs3, stageBs3 []float64) {
// Transfer function uses the negatives of the b coefficients
stageBs1 = functional.Map(functional.Negate, stageBs1)
stageBs2 = functional.Map(functional.Negate, stageBs2)
// Transfer function has a 1 in the denominator
stageBs1[0], stageBs2[0] = 1, 1
// For addition of transfer functions, numerator is stagesA1 * stagesB2 + stagesA2 * stagesB1. Denominator is the same as for cascading.
// Polynomial multiplication of the numerator and denominator of the tranfer functions is done by convolution
stageAs3 = functional.ZipWith(functional.Add, convolve(stageAs1, stageBs2), convolve(stageAs2, stageBs1))
stageBs3 = convolve(stageBs1, stageBs2)
functional.MapInPlace(functional.Negate, stageBs3)
// just for good measure
stageBs3[0] = 0
return
}
// Although b0 is not a used coefficient, space for it is still expected
func ParallelizeFilterStages(stage1, stage2 FilterCoefficients) (stage3 FilterCoefficients) {
// Transfer function uses the negatives of the b coefficients
stage1Bs := functional.Map(functional.Negate, stage1.Bs)
stage2Bs := functional.Map(functional.Negate, stage2.Bs)
// Transfer function has a 1 in the denominator
stage1Bs[0], stage2Bs[0] = 1, 1
// For addition of transfer functions, numerator is stagesA1 * stagesB2 + stagesA2 * stagesB1. Denominator is the same as for cascading.
// Polynomial multiplication of the numerator and denominator of the tranfer functions is done by convolution
stage3.As = functional.ZipWith(functional.Add, convolve(stage1.As, stage2Bs), convolve(stage2.As, stage1Bs))
stage3.Bs = convolve(stage1Bs, stage2Bs)
functional.MapInPlace(functional.Negate, stage3.Bs)
// just for good measure
stage3.Bs[0] = 0
return
}