ROOTCASTLE / ENGINEERING LAB

Deasachd fhiltir

Filtrichean Biquad, plotaichean Bode agus còd C.

LOCAL CALCULATION · RUNS IN THE BROWSER

Filter typeSample rate fs [Hz]Corner / centre frequency f0 [Hz]OrderQuality factor QFixed-point fraction bitsProbe frequency [Hz]

✓ Stable: all poles inside the unit circle

Floating pointQuantized Q14

× poles○ zeros

|H(2kHz)|: -12.37 dB
∠H(2kHz): -136.9°
Section: 1
max |pole|: 0.911594

Section	b0	b1	b2	a1	a2
1	0.0039161235	0.007832247	0.0039161235	-1.8153396	0.83100411
1 · Q14	64	128	64	-29743	13615

/* Low-pass Q 0.7071, f0 1kHz, fs = 48000 Hz. Generated by Rootcastle LAB; verify against your own requirements. */
typedef struct { float b0, b1, b2, a1, a2; float z1, z2; } biquad_t;
static biquad_t stages[1] = {
  { 0.003916123487f, 0.007832246974f, 0.003916123487f, -1.815339612f, 0.8310041056f },
};
float filter_step(float x) {
  for (int i = 0; i < 1; i++) {
    biquad_t *s = &stages[i];
    float y = s->b0 * x + s->z1;
    s->z1 = s->b1 * x - s->a1 * y + s->z2;
    s->z2 = s->b2 * x - s->a2 * y;
    x = y;
  }
  return x;
}

Model and assumptions

Second-order IIR (biquad) sections are designed with the bilinear transform using R. Bristow-Johnson’s “Audio EQ Cookbook” formulas. As the corner approaches fs/2, frequency warping increases the deviation from the analog prototype. 4th- and 6th-order low/high-pass filters are cascaded with Butterworth Q values (the Q input is then unused). Fixed-point results show coefficient quantization only; accumulator overflow, rounding noise and limit cycles must be tested separately.

ω0 = 2π·f0/fs; α = sin ω0 / 2Q; H(z) = (b0 + b1·z⁻¹ + b2·z⁻²) / (1 + a1·z⁻¹ + a2·z⁻²)

Airson a bheil iad airson

Tha biquad ann an sgoilear as co-dhùinte a tha a’ cur ri chlaidheamh a bhith a’ toirt air ais mains hum bho shìgneal sensair (notch 50/60 Hz), a’ cur às an àm-band seasmachadh no a’ dèanamh de na h-èifeachdan ann an circeachd coileanaidh. Cuir an deasachadh seo a chleachdadh, faic mìneachd agus faisean còmhla, an sin dearbhaich na co-eifeachdan agus C code air do chòmhlan fhèin.

Lìonachaisean

Tha lag faise an t-ìre stèileachadh de chùrsa leantainn; còmharraich an margaidh faise ro chur an fhiltir a-steach anns an lùp. Ann an punt-fhìos, tha ceangaladh co-eifeantachd a’ cur polan gu crìoch an chùirn ann an àireamhan f0/fs ìosal; feumaidh leitheid an stòraiche agus coimhead othrach a chlàradh le bhith beò. Chan fhaodaidh e a bhith a’ dèanamh de fhiltir ànaileachd anti-alias: feumaidh aliasing a thràth a chur a-steach ro chomharrachadh an ADC.

References

R. Bristow-Johnson, “Cookbook formulae for audio EQ biquad filter coefficients” (W3C Audio EQ Cookbook) · A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, 3rd ed., ch. 6–7 · S. Butterworth, “On the Theory of Filter Amplifiers”, 1930

Mòdell foghlam. Chan eil na comharrachadh gu h-òmhair airson diùcadh a-mach ri machan-aillean no a thogail leasachaidhean sòisealta.

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