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feat(tracker): spectrum analyzer

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Closes #67
This commit is contained in:
5684185+vsariola@users.noreply.github.com
2025-12-29 23:57:08 +02:00
parent 4d09e04a49
commit 3a7010f897
16 changed files with 977 additions and 211 deletions
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19
patch.go
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@ -251,23 +251,12 @@ func arrDispFunc(arr []string) UnitParameterDisplayFunc {
}
func filterFrequencyDispFunc(v int) (string, string) {
// Matlab was used to find the frequency for the singularity when r = 0:
// % p is the frequency parameter squared, p = freq * freq
// % We assume the singular case r = 0.
// syms p z s T
// A = [1 p;-p 1-p*p]; % discrete state-space matrix x(k+1)=A*x(k) + ...
// pol = det(z*eye(2)-A) % characteristic discrete polynomial
// spol = simplify(subs(pol,z,(1+s*T/2)/(1-s*T/2))) % Tustin approximation
// % where T = 1/(44100 Hz) is the sample period
// % spol is of the form N(s)/D(s), where N(s)=(-T^2*p^2*s^2+4*T^2*s^2+4*p^2)
// % We are interested in the roots i.e. when spol == 0 <=> N(s)==0
// simplify(solve((-T^2*p^2*s^2+4*T^2*s^2+4*p^2)==0,s))
// % Answer: s=±2*p/(T*(p^2-4)^(1/2)). For small p, this simplifies to:
// % s=±p*j/T. Thus, s=j*omega=j*2*pi*f => f=±p/(2*pi*T).
// So the singularity is when f = p / (2*pi*T) Hz.
// In https://www.musicdsp.org/en/latest/Filters/23-state-variable.html,
// they call it "cutoff" but it's actually the location of the resonance
// peak
freq := float64(v) / 128
p := freq * freq
f := 44100 * p / math.Pi / 2
f := math.Asin(p/2) / math.Pi * 44100
return strconv.FormatFloat(f, 'f', 0, 64), "Hz"
}