Understanding High-Pass Filters

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Definition: What is a High-Pass Filter?

High-pass filter (HPF) is a frequency-selective signal processing element that allows vibration components above a specified cutoff frequency to pass through while attenuating (reducing) components below the cutoff frequency. In vibration analysis, high-pass filters are used to remove low-frequency vibration (from unbalance, misalignment) and focus on high-frequency content (from bearing defects, gear mesh, electrical frequencies), or to eliminate sensor mounting resonance effects and DC offsets.

High-pass filters are fundamental components in envelope analysis, anti-aliasing systems, and signal conditioning, enabling extraction of diagnostic information from specific frequency ranges while rejecting unwanted low-frequency components that might mask or overwhelm the signals of interest.

Filter Characteristics

Cutoff Frequency (fc)

• Definition: Frequency where filter response drops to -3 dB (70.7% of passband amplitude)
• Below fc: Frequencies progressively attenuated
• Above fc: Frequencies pass with minimal attenuation
• Selection: Choose fc based on application and frequency content of interest

Filter Slope (Roll-off Rate)

• Rate of attenuation below cutoff frequency
• Expressed in dB per octave or dB per decade
• 1st Order: 6 dB/octave (20 dB/decade) – gentle slope
• 2nd Order: 12 dB/octave (40 dB/decade) – moderate slope
• 4th Order: 24 dB/octave (80 dB/decade) – steep slope
• Higher Order: Sharper transition, better rejection, but more complex

Filter Types

• Butterworth: Maximally flat passband response
• Chebyshev: Sharper cutoff but with ripple in passband
• Bessel: Best time-domain characteristics (minimal phase distortion)
• Elliptic: Sharpest transition but ripple in both passband and stopband

Applications in Vibration Analysis

1. Bearing Defect Detection

Most common application:

• Cutoff: Typically 500-2000 Hz
• Purpose: Remove low-frequency unbalance and misalignment vibration
• Result: Focus on high-frequency bearing impact signals
• Use: First stage in envelope analysis processing

2. Integration for Velocity/Displacement

• When integrating acceleration to velocity or displacement
• HPF at 2-10 Hz removes DC offset and very low frequencies
• Prevents integration errors and drift
• Essential for accurate low-frequency integration

3. Sensor Mounting Resonance Elimination

• Accelerometer mounting resonance (typically 3-10 kHz for magnetic mount)
• HPF removes this resonance artifact
• Ensures measurements represent machine vibration, not sensor effects

4. DC Offset Removal

• HPF with very low cutoff (0.5-2 Hz) removes DC component
• Necessary for proper signal processing
• Prevents FFT errors and integration drift

Practical Implementation

Analog vs. Digital Filters

Analog High-Pass Filters

• Hardware circuits in signal conditioning
• Real-time operation
• Anti-aliasing and sensor conditioning
• Fixed characteristics once designed

Digital High-Pass Filters

• Software-based post-processing
• Adjustable cutoff and filter order
• Can be applied/removed after data collection
• Modern analyzers provide multiple filter options

Selecting Cutoff Frequency

For Bearing Analysis

• Set fc below lowest bearing fault frequency
• Typical: 500-1000 Hz cutoff
• Removes 1×, 2×, gear mesh, etc.
• Passes bearing fault frequencies (typically 50-500 Hz) and their high-frequency modulation

For Integration

• Set fc at 2-5× lowest frequency of interest
• Too low: allows drift
• Too high: attenuates valid low-frequency components
• Typical: 2-10 Hz for general integration

Effects on Measurements

Amplitude Effects

• Frequencies below cutoff reduced in amplitude
• Very low frequencies essentially eliminated
• Frequencies well above cutoff unaffected
• Transition region shows gradual reduction

Phase Effects

• Filters introduce phase shift
• Phase shift frequency-dependent
• Can affect time-domain waveform shape
• Bessel filters minimize phase distortion

Waveform Effects

• Removes low-frequency baseline variations
• Centers waveform around zero
• Can change apparent waveform character
• Important to understand filtering when interpreting waveforms

Combined with Other Filters

High-Pass + Low-Pass = Band-Pass

• HPF blocks low frequencies
• LPF blocks high frequencies
• Combination passes only middle band
• Creates bandpass filter for specific frequency range

High-Pass in Multi-Stage Processing

• Anti-aliasing (low-pass) before digitization
• High-pass for DC removal
• Bandpass for envelope analysis
• Sequential filtering for complex signal conditioning

High-pass filters are essential signal processing tools in vibration analysis, enabling isolation of high-frequency diagnostic information by removing dominant low-frequency components. Understanding high-pass filter characteristics—cutoff frequency, filter order, and effects on amplitude and phase—is crucial for proper application in bearing analysis, signal integration, and any analysis requiring frequency-selective measurement.

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