How Are Envelope Analysis and Bandpass Sampling Related?
Envelope analysis and bandpass sampling are used in very different fields
- Envelope analysis is commonly used in vibration analysis and condition monitoring.
- Bandpass sampling is widely used in RF and communication systems.
At first glance, they appear unrelated. However, both techniques share a common idea. They focus on the information contained within a specific frequency band rather than the entire spectrum.
Both methods exploit the fact that the signal of interest occupies only a limited portion of the frequency spectrum.
The Common Idea: A Band-Limited Signal
Consider a signal concentrated around a carrier frequency
where
- fc is a high-frequency carrier,
- A(t) is a slowly varying modulation signal.
Examples include
- a bearing resonance excited by impacts
- an AM radio signal
- a vibration resonance containing fault information
Both envelope analysis and bandpass sampling focus on this band-limited signal, but they process it differently.
Envelope Analysis Extracts the Modulation
Envelope analysis asks "What information is hidden inside the amplitude variations of this frequency band?"
The typical procedure is
- Bandpass filter around the carrier frequency.
- Extract the envelope (often using the Hilbert transform) → demodulation.
- Analyze the envelope spectrum.
The result is A(t)
which contains
- bearing defect frequencies
- impact repetition rates
- modulation frequencies
In other words, envelope analysis removes the carrier and keeps the modulation.
Bandpass Sampling Preserves the Modulation
Bandpass sampling asks "Can this band-limited signal be sampled at a lower rate without losing information?"
Instead of sampling above 2fc, the signal is sampled at a carefully chosen lower rate.
The carrier band aliases into a lower-frequency region, but the modulation information remains intact.
For example, 940∼960 MHz may be sampled at 80 MHz and folded into 0∼20 MHz without losing the information carried by the signal instead of sampling above 2fc = 2*960 = 1920 MHz.
In other words, bandpass sampling preserves both the carrier and its modulation through controlled aliasing.
Both Exploit Redundancy in the Spectrum
Neither technique needs the entire spectrum.
Envelope analysis recognizes that the fault information exists in the modulation, not in the resonance frequency itself.
Bandpass sampling recognizes that the signal occupies only a narrow frequency band, not the entire range from DC to the carrier frequency.
Thus both methods use prior knowledge of the signal's spectral structure.
A Bearing Fault Example: refer to the MALMIJAL example below
Suppose a bearing defect generates impacts at 120 Hz which excite a resonance at 5000 Hz.
The vibration signal can be modeled as x(t) = A(t) ⋅ cos (2π⋅5000t)
where
- the 5000 Hz resonance is the carrier
- the 120 Hz impacts appear in the modulation A(t)
As a result, the spectrum contains sidebands around the resonance frequency 5000 ± 120, 5000 ± 240, 5000 ± 360,… rather than a single peak at 5000 Hz.
Envelope Analysis
Envelope analysis first isolates the resonance band around 5000 Hz using a band-pass filter. The envelope of the filtered signal is then extracted using rectification or the Hilbert transform.
The FFT of the envelope reveals 120 Hz, 240 Hz, 360 Hz, and other fault frequencies. Thus, envelope analysis converts a high-frequency resonance signal into a low-frequency fault signature that is easier to interpret.
Bandpass Sampling
Notice that the useful information is not the 5000 Hz carrier itself, but the relatively narrow band around it. For example, if the resonance occupies 5000 ± 500 Hz, the signal bandwidth is only B = 1000 Hz.
Although the carrier frequency is 5000 Hz, the information bandwidth is only 1000 Hz.
Therefore, bandpass sampling can intentionally alias the 5000 Hz resonance band to a lower frequency while preserving its modulation structure. As long as the bandpass sampling conditions are satisfied Fs > 2B, the defect information contained in the sidebands remains intact.
After sampling, the carrier frequency may move to a different frequency due to aliasing, but the modulation frequencies (120 Hz, 240 Hz, 360 Hz, ...) are still preserved and can be recovered through envelope analysis.
Conceptually, Both Are Forms of Frequency Translation
There is an interesting conceptual similarity.
Envelope Analysis
Performs a type of demodulation fc → 0. The modulation is moved from around the carrier frequency to baseband.
Bandpass Sampling
Performs a type of aliasing-based frequency translation fc → falias. The carrier band is moved to a lower frequency region through sampling.
Thus both methods effectively relocate information from one frequency region to another.
The difference is that
- envelope analysis intentionally removes the carrier
- bandpass sampling intentionally preserves it
Comparison
| Feature | Envelope Analysis | Bandpass Sampling |
|---|
| Category | Signal-processing technique | Sampling technique |
| Main purpose | Extract amplitude modulation | Reduce sampling rate |
| Application | Fault diagnosis | Signal acquisition |
| Uses aliasing? | No (uses demodulation) | Yes (intentionally) |
| Uses modulation? | Yes | No |
| Remove carrier? | Yes | No |
| Preserve carrier? | No | Yes |
| Reveals defect frequencies? | Yes | No |
| Reduces ADC requirements? | No | Yes |
| Typical field | Vibration analysis | RF communications |
MALMIJAL Examples (Fs = 50kHz)
Envelope Analysis
Original data and it envelope curve
FFTs of original data and its envelope
Bandpass Sampling
Original data and its downsampling → Bandpass sampling (controlled aliasing) → same profile as envelope curve
FFT of Bandpass Sampling
FFT of envelope(set x-axis limit) vs FFT of bandpass sampling (same result)
Intuitive Interpretation
Envelope analysis asks "What is hidden inside this resonance band?"
Bandpass sampling asks "Can I acquire this resonance band more efficiently?"
One extracts information from the band, while the other acquires the band efficiently.
Conclusion
Although envelope analysis and bandpass sampling serve different purposes, they share a common philosophy: both focus on a specific frequency band and exploit the fact that the information of interest occupies only a small portion of the spectrum.
Envelope analysis extracts the modulation hidden within a carrier, whereas bandpass sampling preserves that carrier and its modulation while reducing the required sampling rate through controlled aliasing.
In one sentence, envelope analysis extracts the information contained in a frequency band, while bandpass sampling efficiently acquires that same frequency band by intentionally translating it to a lower-frequency region.
Suggested Further Reading
##You may also find these topics helpful:
How Are Envelope Analysis and Bandpass Sampling Related?
Envelope analysis and bandpass sampling are used in very different fields
At first glance, they appear unrelated. However, both techniques share a common idea. They focus on the information contained within a specific frequency band rather than the entire spectrum.
Both methods exploit the fact that the signal of interest occupies only a limited portion of the frequency spectrum.
The Common Idea: A Band-Limited Signal
Consider a signal concentrated around a carrier frequency
where
Examples include
Both envelope analysis and bandpass sampling focus on this band-limited signal, but they process it differently.
Envelope Analysis Extracts the Modulation
Envelope analysis asks "What information is hidden inside the amplitude variations of this frequency band?"
The typical procedure is
The result is A(t)
which contains
In other words, envelope analysis removes the carrier and keeps the modulation.
Bandpass Sampling Preserves the Modulation
Bandpass sampling asks "Can this band-limited signal be sampled at a lower rate without losing information?"
Instead of sampling above 2fc, the signal is sampled at a carefully chosen lower rate.
The carrier band aliases into a lower-frequency region, but the modulation information remains intact.
For example, 940∼960 MHz may be sampled at 80 MHz and folded into 0∼20 MHz without losing the information carried by the signal instead of sampling above 2fc = 2*960 = 1920 MHz.
In other words, bandpass sampling preserves both the carrier and its modulation through controlled aliasing.
Both Exploit Redundancy in the Spectrum
Neither technique needs the entire spectrum.
Envelope analysis recognizes that the fault information exists in the modulation, not in the resonance frequency itself.
Bandpass sampling recognizes that the signal occupies only a narrow frequency band, not the entire range from DC to the carrier frequency.
Thus both methods use prior knowledge of the signal's spectral structure.
A Bearing Fault Example: refer to the MALMIJAL example below
Suppose a bearing defect generates impacts at 120 Hz which excite a resonance at 5000 Hz.
The vibration signal can be modeled as x(t) = A(t) ⋅ cos (2π⋅5000t)
where
As a result, the spectrum contains sidebands around the resonance frequency 5000 ± 120, 5000 ± 240, 5000 ± 360,… rather than a single peak at 5000 Hz.
Envelope Analysis
Envelope analysis first isolates the resonance band around 5000 Hz using a band-pass filter. The envelope of the filtered signal is then extracted using rectification or the Hilbert transform.
The FFT of the envelope reveals 120 Hz, 240 Hz, 360 Hz, and other fault frequencies. Thus, envelope analysis converts a high-frequency resonance signal into a low-frequency fault signature that is easier to interpret.
Bandpass Sampling
Notice that the useful information is not the 5000 Hz carrier itself, but the relatively narrow band around it. For example, if the resonance occupies 5000 ± 500 Hz, the signal bandwidth is only B = 1000 Hz.
Although the carrier frequency is 5000 Hz, the information bandwidth is only 1000 Hz.
Therefore, bandpass sampling can intentionally alias the 5000 Hz resonance band to a lower frequency while preserving its modulation structure. As long as the bandpass sampling conditions are satisfied Fs > 2B, the defect information contained in the sidebands remains intact.
After sampling, the carrier frequency may move to a different frequency due to aliasing, but the modulation frequencies (120 Hz, 240 Hz, 360 Hz, ...) are still preserved and can be recovered through envelope analysis.
Conceptually, Both Are Forms of Frequency Translation
There is an interesting conceptual similarity.
Envelope Analysis
Performs a type of demodulation fc → 0. The modulation is moved from around the carrier frequency to baseband.
Bandpass Sampling
Performs a type of aliasing-based frequency translation fc → falias. The carrier band is moved to a lower frequency region through sampling.
Thus both methods effectively relocate information from one frequency region to another.
The difference is that
Comparison
MALMIJAL Examples (Fs = 50kHz)
Envelope Analysis
Bandpass Sampling
Intuitive Interpretation
Envelope analysis asks "What is hidden inside this resonance band?"
Bandpass sampling asks "Can I acquire this resonance band more efficiently?"
One extracts information from the band, while the other acquires the band efficiently.
Conclusion
Although envelope analysis and bandpass sampling serve different purposes, they share a common philosophy: both focus on a specific frequency band and exploit the fact that the information of interest occupies only a small portion of the spectrum.
Envelope analysis extracts the modulation hidden within a carrier, whereas bandpass sampling preserves that carrier and its modulation while reducing the required sampling rate through controlled aliasing.
In one sentence, envelope analysis extracts the information contained in a frequency band, while bandpass sampling efficiently acquires that same frequency band by intentionally translating it to a lower-frequency region.
Suggested Further Reading
##You may also find these topics helpful: