One pole, one zero LP/HP

code
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void SetLPF(float fCut, float fSampling)
{
    float w = 2.0 * fSampling;
    float Norm;

    fCut *= 2.0F * PI;
    Norm = 1.0 / (fCut + w);
    b1 = (w - fCut) * Norm;
    a0 = a1 = fCut * Norm;
}

void SetHPF(float fCut, float fSampling)
{
    float w = 2.0 * fSampling;
    float Norm;

    fCut *= 2.0F * PI;
    Norm = 1.0 / (fCut + w);
    a0 = w * Norm;
    a1 = -a0;
    b1 = (w - fCut) * Norm;
}

Where
out[n] = in[n]*a0 + in[n-1]*a1 + out[n-1]*b1;

Comments

what is n? lol...sorry but i mean this seriously! ;)

n is the index of sample being considered.

out[] is an array of samples being output, and in[] is the input array. you would construct a loop such that:
[Pseudocode]
loop n{0..numsamples-1}
  out[n] = in[n]*a0 + in[n-1]*a1 + out[n-1]*b1;
end loop;
[/Pseudocode]

You will need some cleverness so that [n-1] doesn't cause an index error when n=0, but I'll leave that to you :)

whoops - sorry, of course n = number... stupid me ;)
interesting code, i will see if can adapt that to delphi, shouldn´t be a big deal :)

i assume i dont need to place either setHPF or LPF into the samples loop, just the block itself?

absolutey - set the coefficients outside of the loop. There is the case of changes being made whilst the loop is running, depends what platform/host you are writing for.

I'm a delphi code as well. Feel free to use my posted address if you need to :) DSP

Shouldn't that be float w = 2*PI*fSampling; ???

In which case we can simplify:

void SetLPF(float fCut, float fSampling)
{
a0 = fCut/(fSampling+fCut);
a1 = a0;
b1 = (fSampling-fCut)/(fSampling+fCut);
}

void SetHPF(float fCut, float fSampling)
{
a0 = fSampling/(fSampling+fCut);
a1 = -a0;
b1 = (fSampling-fCut)/(fSampling+fCut);
}

You can keep the norm = 1/(fSampling+fCut) if you like.
  • Date: 2020-05-23
  • By: JoergBitzer
The equation of the original contributor is correct. It is a first order Butterworth-Filter
H(s') = 1/(1+s') and then denormalized s' = s/wcut and transformed by the bilinear transform
s = 2f_s (z-1)/(z+1). Only the tan-prewarp is missing for fcut/wcut.