Before an acoustic signal hits the FFT, it typically passes 2–3 filter stages – anti-aliasing, drift high-pass, bandpass on the band of interest. Filters are invisible helpers without which no clean evaluation succeeds.

Two families: IIR and FIR

IIR (Infinite Impulse Response): classical analog filters, digitally emulated. Very efficient – few coefficients for steep slopes. Drawback: nonlinear phase.

H(z) = (Σ bk z−k) / (1 + Σ ak z−k)

FIR (Finite Impulse Response): no feedback, only forward coefficients. Linear phase (no signal distortion). Drawback: many more coefficients for the same slope.

H(z) = Σ bk z−k

Comparison

CriterionIIRFIR
Compute for same slopelow (10–30×)high
Phasenonlinearlinear
Stabilitycritical (poles)always stable
Implementationmediumeasy
Ideal usereal-time level meteringmodal analysis, phase-critical work

Standard filter types

Butterworth: maximally flat passband. Classic for clean level measurement.

Chebyshev I: steeper than Butterworth, ripple in passband.

Chebyshev II: ripple in stopband, smooth passband.

Bessel: optimal phase linearity for IIR, gentler slopes. Standard when pulse shapes must be preserved.

Elliptic (Cauer): steepest possible slopes, ripple in both bands.

Use cases

  1. Anti-aliasing low-pass before ADC, typ. 8th-order Butterworth or Elliptic.
  2. High-pass against drift on accelerometers (5–20 Hz).
  3. Bandpass on the relevant range to save data and CPU.
  4. A-weighting filter (IEC 61672) for dB(A) level metering.
  5. Octave / third-octave filters for noise standards.

SonicTC.DSP filter chain example

Typical chain for tool-wear monitoring:

  1. Analog anti-aliasing low-pass before ADC.
  2. IIR Butterworth 4th order, fc = 100 Hz (drift removal).
  3. IIR Butterworth 6th order, 1–8 kHz bandpass (tool engagement).
  4. FFT with Hann window.
  5. A-weighting (FIR) if dB(A) needed.

What to remember

  1. IIR efficient, FIR clean – choose by application.
  2. Butterworth is the safe default; Elliptic for extreme slopes.
  3. Phase distortion can heavily alter signals – use FIR or Bessel for modal analysis.
  4. Filters save data, CPU and prevent aliasing – they are not optional.