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Isolating Tooth-Pass Harmonics in a 95 dB Industrial Workshop Using Real-Time DSP Bandpass Filters
Category: Acoustic AI • Published: 2026-08-28 • By Muhammad Ali
A functioning commercial CNC workshop is an acoustic nightmare. Nearby, a $15\text{ kW}$ dual-bag dust collector rumbles at $120\text{ Hz}$, air compressors cycle with $85\text{ dB}$ pressure pulses, and neighboring saws generate broadband white noise.
Capturing subtle cutting tool vibration requires rigorous real-time digital filtering before signal ingestion into our neural models.
### Filter Topology: Cascaded 4th-Order Butterworth IIR
We implement a real-time cascaded digital Infinite Impulse Response (IIR) Butterworth filter. We select Butterworth topology over Chebyshev because it exhibits a maximally flat passband response with zero ripple, preserving the relative amplitude ratios between fundamental frequencies and harmonic overtones.
$\left| H(j\omega) \right| = \frac{1}{\sqrt{1 + \left(\frac{\omega}{\omega_c}\right)^{2n}}}$
Where $n = 4$ provides a steep $-80\text{ dB/decade}$ rolloff, completely eliminating low-frequency motor hum and structural floor vibrations below $150\text{ Hz}$.
### RPM-Synchronous Notch Tracking
Because spindle speed is dynamically commanded via G-code (`S18000`, `S21000`), our filter center frequency tracks the live RPM telemetry stream. As the spindle accelerates, the filter passband shifts in lockstep, isolating the tooth-pass harmonic with high signal-to-noise ratio ($SNR > 28\text{ dB}$).