What is a Low-Pass Filter? Anti-Aliasing and Smoothing • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors What is a Low-Pass Filter? Anti-Aliasing and Smoothing • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors

What is a Low-Pass Filter? Anti-Aliasing and Smoothing

Published by admin on

Understanding Low-Pass Filters

Definition: What is a Low-Pass Filter?

Low-pass filter (LPF) is a frequency-selective signal processing element that allows vibration components below a specified cutoff frequency to pass through while attenuating (reducing or blocking) components above the cutoff frequency. In vibration analysis, low-pass filters serve critical functions including anti-aliasing (preventing false frequencies in digital systems), noise reduction, and isolating low-frequency vibration components for focused analysis.

Low-pass filters are perhaps the most commonly used filters in vibration instrumentation, present in every digitizing system as anti-aliasing filters and available as analysis tools for smoothing data, removing high-frequency noise, and focusing on low-frequency phenomena.

Filter Characteristics

Cutoff Frequency (fc)

  • Definition: Frequency where filter response drops to -3 dB (70.7% amplitude)
  • Below fc (Passband): Frequencies pass with minimal attenuation
  • Above fc (Stopband): Frequencies progressively attenuated
  • Transition Band: Region around fc where attenuation increases

Filter Order and Roll-Off

  • 1st Order: 6 dB/octave (20 dB/decade) – gradual roll-off
  • 2nd Order: 12 dB/octave (40 dB/decade) – moderate
  • 4th Order: 24 dB/octave (80 dB/decade) – steep
  • 8th Order: 48 dB/octave (160 dB/decade) – very steep
  • Higher Order: Sharper transition, better stopband rejection

Filter Response Types

  • Butterworth: Maximally flat passband, no ripple
  • Chebyshev: Sharper cutoff, allows passband ripple
  • Bessel: Linear phase (minimal waveform distortion)
  • Elliptic: Sharpest transition, ripple in both bands

Primary Applications

1. Anti-Aliasing (Most Critical)

Prevents false frequencies in digital systems:

  • Purpose: Block frequencies above Nyquist frequency (half sample rate)
  • Requirement: Before analog-to-digital conversion
  • Typical Cutoff: 0.4-0.8 × (Sample Rate / 2)
  • Steepness: Typically 8th order or higher for good aliasing rejection
  • Critical: Inadequate anti-aliasing creates false spectral peaks

2. Noise Reduction

  • Remove high-frequency electrical noise
  • Filter out sensor cable noise
  • Smooth data for trending
  • Improve signal-to-noise ratio for low-frequency components

3. Frequency Range Limitation

  • Focus analysis on frequency range of interest
  • Example: 0-100 Hz analysis for low-speed machinery
  • Removes irrelevant high-frequency content
  • Reduces data processing and storage requirements

4. Integration Preparation

  • Before integrating acceleration to velocity
  • Remove very high frequencies (noise that would be amplified)
  • Typical cutoff: 1000-5000 Hz depending on application
  • Prevents noise amplification in integration

Selecting Cutoff Frequency

Anti-Aliasing Applications

  • Rule: fc = 0.4 × Sample Rate (conservative) to 0.8 × Sample Rate (aggressive)
  • Example: 10 kHz sample rate → fc = 4000 Hz
  • Criterion: Stopband attenuation > 60 dB at Nyquist frequency

Analytical Applications

  • Set fc just above highest frequency of interest
  • For low-frequency analysis (0-200 Hz): fc = 200-300 Hz
  • For unbalance only (1×): fc = 5-10× running speed
  • Leave margin for filter transition band

Noise Reduction

  • Identify noise frequency range from spectrum
  • Set fc to pass signal frequencies, reject noise frequencies
  • Balance between noise removal and signal preservation

Effects on Measurements

Amplitude Domain

  • Passband: Minimal amplitude change (< 0.5 dB typically)
  • Stopband: Strong attenuation (40-80 dB or more)
  • Overall Level: Reduces overall vibration if high frequencies present

Time Domain

  • Waveform smoothed (high-frequency variations removed)
  • Sharp edges or spikes rounded
  • Transient response (filter ringing) can affect waveform shape
  • Phase distortion can affect waveform interpretation

Frequency Domain

  • Spectrum shows reduced amplitudes above cutoff
  • High-frequency peaks diminished or eliminated
  • Noise floor lowered if noise was high-frequency

Common Issues and Solutions

Inadequate Anti-Aliasing

  • Symptom: False low-frequency peaks in spectrum
  • Cause: High frequencies folding back below Nyquist
  • Solution: Use steeper filter, increase sample rate, verify filter functioning

Cutoff Too Low

  • Symptom: Valid high-frequency signals attenuated
  • Example: Bearing frequencies reduced by overly aggressive LPF
  • Solution: Increase cutoff frequency, use gentler filter slope

Filter Artifacts

  • Ringing: Oscillations in time domain from sharp filter cutoff
  • Phase Distortion: Waveform shape changes from phase shifts
  • Solution: Use Bessel filter for critical waveform applications

Complementary Filters

Low-Pass vs. High-Pass

  • Low-Pass: Passes low frequencies, blocks high
  • High-Pass: Passes high frequencies, blocks low
  • Complementary: Used together for band-pass filtering

Band-Pass Filter

  • Combination: HPF + LPF
  • Passes only frequencies in specified band
  • Rejects both below and above band
  • Essential for envelope analysis

Low-pass filters are fundamental components in vibration measurement systems, serving essential functions from anti-aliasing protection to noise reduction and frequency range selection. Understanding low-pass filter operation, proper cutoff frequency selection, and effects on measured signals is crucial for accurate vibration analysis and avoiding measurement artifacts in digital data acquisition systems.

← Back to Main Index

Categories: GlossaryVibration Diagnostics
WhatsApp