Bearing defects produce vibration signatures that are often buried beneath much stronger signals from shaft imbalance, gear meshing, and structural resonances. A raw FFT spectrum of a machine with a developing outer race spall may show no obvious peak at the expected BPFO frequency — the defect signal is simply too small relative to the dominant low-frequency vibration. Envelope analysis (also called amplitude demodulation or high-frequency resonance technique, HFRT) solves this problem by extracting the repetition rate of high-frequency impulses generated by defect impacts. It is one of the most powerful tools in bearing diagnostics, and understanding how it works is essential for anyone interpreting vibration data from bearing monitoring systems.
The Problem Envelope Analysis Solves
When a rolling element strikes a spall on a raceway, the impact produces a brief, broadband impulse — a short burst of energy spanning a wide frequency range, often from a few hundred hertz to well above 10 kHz. This impulse excites structural resonances in the bearing housing and sensor mount, producing a short burst of high-frequency ringing that decays quickly before the next rolling element arrives.
In the time domain, each impulse looks like a damped oscillation (a brief ring-down). The repetition rate of these impulses equals the bearing defect frequency — BPFO for an outer race fault, BPFI for an inner race fault, and so on. However, in a standard FFT of the raw signal, the defect frequency information is spread across a wide band of high frequencies rather than concentrated at a single low-frequency peak. The standard FFT shows energy at the structural resonance frequencies but does not clearly reveal the repetition rate. Meanwhile, the direct BPFO frequency component in the low-frequency region of the raw spectrum is often too weak to detect against the background of rotor-dynamic vibration.
Envelope analysis extracts the repetition rate from the high-frequency content, converting the periodic bursts of high-frequency energy into a clean low-frequency signal at the defect frequency.
Step-by-Step: How Envelope Analysis Works
Step 1: Acquire a Raw Time Waveform
The process starts with a high-frequency vibration measurement — a time-domain waveform sampled at a rate sufficient to capture the high-frequency structural resonance excited by the defect impacts. For most industrial bearings, this means sampling at 20 kHz or higher (supporting a Nyquist frequency of 10 kHz or above). The waveform must be long enough to contain many complete cycles of the defect frequency. For a BPFO of 107 Hz, a 1-second waveform contains approximately 107 impulse events — adequate for reliable demodulation.
Step 2: Bandpass Filter Around a Structural Resonance
The raw waveform contains energy at all frequencies: shaft speed harmonics, gear mesh, electrical noise, and the bearing defect impulses. The key step is to apply a bandpass filter that isolates a frequency band where the defect impulses dominate. This band is typically centered on a structural resonance of the bearing housing — often in the 2–10 kHz range — where the impulse energy is concentrated and the competing low-frequency vibration has little content.
Selecting the correct bandpass center frequency and bandwidth is the most critical engineering judgment in envelope analysis. A poorly chosen band may exclude the resonance where defect energy concentrates, or include interference from other sources (such as gear mesh harmonics). Experienced analysts identify the resonant response using an initial broadband spectrum and selecting the frequency region where impulsive energy is evident.
Typical bandpass settings:
- Center frequency: 2,000–10,000 Hz (depends on bearing size, housing geometry, sensor mount)
- Bandwidth: 500–5,000 Hz (narrower bands improve signal-to-noise ratio but risk excluding defect energy)
- Filter type: Butterworth or Chebyshev, 4th to 8th order
Step 3: Rectify the Filtered Signal (Full-Wave Rectification)
After bandpass filtering, the signal consists of bursts of high-frequency oscillation at the structural resonance frequency. Each burst corresponds to one defect impact. To extract the repetition rate, the next step is to take the absolute value of the filtered signal (full-wave rectification) or, equivalently, compute the analytic signal using the Hilbert transform and extract its magnitude (the envelope).
The Hilbert transform approach is standard in modern digital signal processing. Given the bandpass-filtered signal x(t), the analytic signal is:
z(t) = x(t) + j × H[x(t)]where H[x(t)] is the Hilbert transform of x(t) and j is the imaginary unit. The envelope is the magnitude:
envelope(t) = |z(t)| = sqrt(x(t)² + H[x(t)]²)The resulting envelope signal is a smooth, slowly varying function that traces the amplitude of the high-frequency bursts. It oscillates at the defect frequency — the repetition rate of the impulses.
Step 4: Low-Pass Filter the Envelope
The raw envelope may contain residual high-frequency content from incomplete demodulation. A low-pass filter (cutoff typically 500–1,000 Hz, well above the highest expected defect frequency) cleans up the envelope signal. This step is optional in some implementations but improves the clarity of the final envelope spectrum.
Step 5: Compute the FFT of the Envelope
The final step is to compute the FFT of the envelope signal. This envelope spectrum displays peaks at the frequencies corresponding to the repetition rates of the impulses — that is, at the bearing defect frequencies and their harmonics. A peak at BPFO with harmonics at 2× BPFO and 3× BPFO clearly indicates an outer race defect. A peak at BPFI with sidebands at ± shaft speed indicates an inner race defect.
The envelope spectrum is dramatically cleaner than the raw FFT spectrum for bearing defect identification. The dominant shaft-speed harmonics, gear mesh frequencies, and other low-frequency content have been removed by the bandpass filter in Step 2. What remains is purely the repetition pattern of the defect impacts.
Why Envelope Analysis Detects Faults Earlier
A developing bearing defect — a microscopic spall a few hundred micrometers across — produces impulses with very small energy relative to the overall machine vibration. In the raw spectrum, the BPFO component might be 40–60 dB below the dominant 1× shaft-speed peak. It is undetectable against the noise floor.
But in the high-frequency band (say, 3–8 kHz), the machine produces relatively little vibration. The defect impulses excite the structural resonance in this band and temporarily dominate the signal. The signal-to-noise ratio of the defect signature is much higher in the high-frequency band than in the low-frequency raw spectrum. By bandpass filtering into this band and demodulating, envelope analysis exploits this frequency-domain signal-to-noise advantage to reveal defects that are invisible in the raw FFT.
Practical experience shows that envelope analysis can detect bearing defects 2–6 months earlier than raw spectral analysis, depending on machine speed, load, and bearing type. For condition-based maintenance programs, this additional lead time is the difference between a planned bearing replacement during a scheduled outage and an unplanned failure that shuts down a production line.
Requirements for Effective Envelope Analysis
Sufficient Sampling Rate
The sensor and data acquisition system must capture the high-frequency content that envelope analysis depends on. If the structural resonance excited by defect impacts is at 5 kHz, the system must sample at 10 kHz or higher (Nyquist criterion), and the sensor mounting must faithfully transmit vibration at that frequency. As discussed in detail in our article on sensor mounting methods, stud mounting or thin-adhesive mounting is necessary to preserve the high-frequency bandwidth that makes envelope analysis effective.
Sensor Bandwidth
The accelerometer must have a flat frequency response extending to at least 5 kHz, preferably 10 kHz. Most industrial piezoelectric accelerometers meet this requirement easily. MEMS accelerometers vary widely — consumer-grade MEMS devices may roll off above 1–3 kHz, while industrial MEMS sensors extend to 5–10 kHz. Systems like Fault Ledger that are designed specifically for bearing diagnostics select sensors and sampling rates to ensure adequate high-frequency capture for envelope analysis, typically sampling at 25.6 kHz or higher to support demodulation bands up to 10 kHz.
Waveform Capture
Envelope analysis requires the raw time-domain waveform, not just pre-computed spectral summary data. Some low-cost IoT vibration sensors compute overall vibration level (RMS velocity) or a coarse FFT on-board and transmit only summary statistics. These cannot support envelope analysis because the high-frequency time-domain information has been discarded. Effective envelope analysis requires either on-board DSP that performs the demodulation locally or transmission of the raw waveform to a cloud or edge platform for processing.
Common Pitfalls
Wrong Bandpass Selection
If the bandpass filter is centered on a frequency where gear mesh or electrical noise dominates instead of bearing defect impulses, the envelope spectrum will show gear mesh frequency or electrical line frequency instead of defect frequencies. The analyst must identify the frequency band where defect impulse energy is concentrated — this requires examining the raw spectrum for evidence of impulsive excitation (broadband humps or raised noise floor near structural resonances).
Insufficient Spectral Resolution
The envelope spectrum must have sufficient frequency resolution to separate defect frequencies from nearby harmonics of shaft speed. For a BPFO of 107 Hz and a shaft speed of 30 Hz (3.57× shaft speed), the nearest shaft harmonic is 3× (90 Hz) or 4× (120 Hz). A frequency resolution of 1 Hz or better is adequate. But for slow-speed machinery (below 100 RPM), defect frequencies may be below 10 Hz and closely spaced, requiring resolutions of 0.1 Hz or better — which demands waveform lengths of 10 seconds or more.
Confusing Defect Frequencies with Other Sources
Not every peak in the envelope spectrum is a bearing defect. Periodic impacts from other sources — loose bolts, rubbing seals, cavitation — can produce envelope spectrum peaks. Confirmation requires matching peaks to calculated defect frequencies for the specific bearing geometry, checking for harmonics (2×, 3× the defect frequency), and looking for expected sideband patterns (shaft-speed sidebands around BPFI for inner race defects).
Envelope Analysis in IoT Monitoring Architectures
For permanently installed IoT bearing monitoring systems, envelope analysis can be implemented either at the edge (on the sensor node or gateway) or in the cloud. Edge processing reduces data transmission requirements — only the envelope spectrum or demodulated waveform needs to be sent, not the full high-frequency raw waveform. Cloud processing allows more flexible algorithm tuning and reprocessing of historical data with updated parameters.
Some architectures combine both approaches: the edge performs real-time envelope analysis for immediate alarming, while the full raw waveform is captured periodically or on trigger and uploaded for detailed cloud-based diagnostics. Fault Ledger captures and stores raw high-frequency waveforms alongside processed envelope spectra, enabling both automated fault detection and after-the-fact forensic analysis when the specific failure mode or root cause needs to be determined.
Conclusion
Envelope analysis transforms raw vibration data into bearing-specific diagnostic information by extracting the repetition rate of high-frequency defect impulses. The technique — bandpass filter, demodulate (Hilbert transform), FFT — is conceptually simple but demands careful parameter selection and adequate measurement hardware: sufficient sampling rate, sensor bandwidth, and mechanical coupling quality. When implemented correctly, it detects bearing defects months earlier than raw spectral analysis, giving maintenance teams the lead time to plan repairs rather than react to failures. For any serious bearing monitoring program, envelope analysis is not optional — it is foundational.