Zero-Phase Channel Filtering

Example: a triangle wave on channel 1 is band-pass filtered from 100 to 250 Hz with order 16; the high-frequency content is cleanly removed, as the before-and-after waveforms and spectra show.

Screen layout

Filter types

Key functions

• Four views compare the waveform and spectrum before and after filtering without switching windows.
• Adjustable order (1–64) sets the steepness of the transition: low orders give a gradual transition, high orders approach an ideal brick wall.
• The statistics table calculates the RMS before and after filtering and the attenuation in dB for every frame.
• Linked to the main window: the channel waveform and FFT spectrum are read from the main acquisition arrays, and the filtered spectrum uses the same window scaling as the main spectrum.
• Excel export of the filter parameters (type, order, cut-offs) and the original and filtered spectra of all selected channels.
• Stay on top, double-click to maximize any plot, built-in help.

Preprocessing before fault diagnosis

Bearing and gearbox fault signatures are often buried in strong background noise. Band-pass filtering first extracts the diagnostic band, for example around a bearing outer-race frequency; envelope demodulation and zoom analysis then give more reliable conclusions.

Removing supply and environmental interference

50 Hz supply interference and its harmonics are the most common contamination in field tests. A band-stop filter removes 50 Hz precisely (f1 = 48, f2 = 52) and keeps all other content. Because the algorithm is zero-phase, the waveform does not shift in time and events can still be located exactly.

Sensor signal conditioning

• High-pass: remove the DC offset and low-frequency thermal drift of piezoelectric accelerometers.
• Low-pass: remove unwanted high-frequency components in already sampled data. Prevent aliasing with the acquisition hardware and sampling setup; post-acquisition filtering cannot undo aliasing.

Isolating a structural resonance band

Band-pass filtering isolates one resonance band so that its time response, such as beating or decaying oscillation, can be observed, supporting modal analysis and resonance investigation.

Acoustic band analysis

Separate the band of interest, for example 500 Hz to 4 kHz for speech interference, together with the acoustic functions (frequency weighting, octave analysis, sound quality).

Training

The four views show the effect of each parameter immediately and explain cut-off frequency and filter order clearly.

Zero-phase filtering

Filter delay and phase response depend on the design:

• Causal filtering generally introduces delay, which must be accounted for when locating events.
• Some filters have nonlinear phase; a linear-phase FIR filter has constant group delay within its pass band. Filtering still changes the waveform by changing its frequency content.

The source describes a real, non-negative, even-symmetric mask applied to a complete FFT frame:

1. Transform the complete frame to the frequency domain with an FFT.
2. Build a real, non-negative, even-symmetric mask H(f), with equal magnitude at positive and negative frequencies.
3. Multiply the spectrum by the mask point by point and transform back with an inverse FFT.

A real, non-negative, even mask adds no phase shift to retained frequency components. Whole-frame filtering nevertheless has finite-record boundary effects and can change peaks and waveform shape. It is not generally equivalent to forward-backward filtering: applying a filter twice changes its magnitude response as well as its phase. Inspect the frame boundaries and validate timing for the measurement task.

Butterworth response and filter order

The mask magnitude follows the maximally flat Butterworth response, −3 dB at the cut-off frequency fc:

Low-pass: |H(f)| = 1 / √(1 + (f / fc)^(2N)) High-pass: |H(f)| = 1 / √(1 + (fc / f)^(2N))

N is the filter order (1–64). The stop-band slope is 6N dB per octave; order 10 gives 60 dB per octave.

Exponents are computed in logarithmic space with upper and lower limits (values beyond them are set to 0 or 1), so no order or frequency ratio causes overflow.

Source-reported numerical checks

The supplied manual reports the following NumPy examples. The test code, inputs and T8 software implementation were not independently validated for this website; these values are illustrative source results, not Vectalen verification evidence:

• Zero-phase mask: no added phase shift to retained components; changed spectral content and frame boundaries can still alter waveform shape and peaks.
• Visible effect: four views and live RMS and attenuation statistics.
• Adjustable boundaries: order 1 to 64, from gradual transitions to brick-wall cut-offs.
• Eight channels in parallel, refreshed with every acquired frame.
• Data ready for reports: filter parameters and complete original and filtered spectra in Excel.
• Part of the T8 analysis platform: shares data and window scaling with the spectrum, fault diagnosis, order tracking and acoustic functions.

Open channel filtering from the main menu (or the corresponding extended analysis menu). The window loads the current frame and draws it.

1. Select channels. Disabled channels are grayed out.
2. Select the filter type: band-pass to view one band; band-stop to remove one band such as 50 Hz interference; low-pass to remove high-frequency spikes; high-pass to remove DC or low-frequency drift.
3. Set the order and cut-offs. Orders 4–10 suit general diagnosis; use 32–64 for steep boundaries, for example to separate two adjacent components. f1 is the lower edge for band-pass and band-stop and the cut-off for high-pass; f2 is the upper edge for band-pass and band-stop and the cut-off for low-pass.
4. Refresh and check. The window refreshes after any change, or press Refresh. The statistics table shows RMS before and after and the attenuation for each channel; if the attenuation is as expected, the settings are correct.
5. Read and export. Upper views show the original waveform and spectrum, lower views the filtered ones, aligned point by point. Double-click a plot to maximize it. Export all data creates an Excel file with the filter parameters and all spectra.

Recommended settings