Undersampling vs Bandpass Sampling Explained
Sampling is usually explained using the Nyquist rule. Sample at least 2× the highest frequency, but in practice, things are more interesting.
Sometimes we intentionally sample below Nyquist!
What Is Undersampling?
Undersampling happens when sampling rate is less than 2× the highest frequency
Result
- Aliasing occurs
- Signal gets distorted
Key Idea
Intuition
“Sampling too slow → information overlaps”
What Is Bandpass Sampling?
Bandpass sampling is a controlled form of undersampling.
Done intentionally!
Key Idea
If the signal is band-limited (not from 0 Hz)
You can sample below Nyquist without losing information
How Bandpass Sampling Works
Bandpass signals can be shifted (aliased) into baseband.
Concept
- Sampling causes frequency-folding
- But if controlled → no overlap
Key Conditions
- Aliased bands must NOT overlap, bandpass filtering required for sure
- Bandpass sampling rate must be greater than 2 x bandwidth(B)
- Unlike standard baseband sampling, the sampling condition here is not based on 2fmax.
Frequency Folding (Aliasing)
When sampling, frequencies fold into lower range.
Relationship
Alias Frequency = | Signal frequency - Closest sampling frequency Harmonic |
Meaning
- Original frequency shifts
- Appears at new location
MALMIJAL Example
- Signal range: 95 ~ 100Hz with white noise, Fs = 3000Hz higher than Nyquist frequency (200Hz)
- You don’t need 3000 Hz sampling, instead 30Hz ( > 2B = 10) downsampling to make intentional aliasing
- Falias= | f - nFs |
- 95 → | 95 - 3*30 | = 5Hz
- 100 → | 100 - 3*30 | = 10Hz
x(t) = sin(2π 95 t) + 0.8sin(2π 100 t) + white noise with Fs = 3000Hz (no alliasing)
Apply bandpass filter (85 ~ 110Hz band) to prevent aliasing overlap caused by white noise,
then downsampling to 30Hz for intentional aliasing (frequency folding or shifted into baseband)
FFT of Noisy signal with 3000Hz sample rate (95 and 100Hz peaks)
FFT of Noisy signal with 3000Hz sample rate (95 and 100Hz peaks, frequency axis limited)
FFT of intentional aliasing with 30Hz sample rate (5 and 10Hz peaks), almost same information as above
No information lost when bandpass filtering, showed without noise for clarity
- uncheck Added Noise of sine wave nodes
- ignore bandpass filtering (select Ignore of light coral node property)
Bandpass filtering does not cause information loss if the signal is clearly within the passband
Key Difference
| Features | Undersampling | Bandpass Sampling |
|---|
| Intentional or not | Occurs unintentionally | Intentionally performed |
| Result | Distortion/aliasing | Desired signal translation |
| Control | Not controlled | Carefully controlled |
| Typical usage | Usually avoid | Commonly used in RF systems |
Real-World Applications
RF Communication
- High-frequency signals sampled at lower rate → Reduced cost, power, data rate
- Sample a high-frequency RF signal at a much lower rate and let aliasing shift it to baseband
- “Select only the desired channel and reject everything else”
Falias = | 960 - 12*80 | = 0MHz, | 950 - 12*80 | = 10MHz, | 940 - 12*80 | = 20MHz
Vibration Analysis
- In vibration analysis, many physical phenomena appear in very narrow frequency bands
- “Keep only the meaningful signal components”
Spectrum Analysis
- Efficient data acquisition
- “Sample only what is necessary”
Key Takeaways
- Undersampling → unwanted aliasing
- Bandpass sampling → controlled aliasing
- Key condition → no overlap
- Useful for narrowband signals
Conclusions
Undersampling normally causes aliasing and distortion because the sampling rate is lower than twice the highest frequency component.
- In most cases, undersampling is undesirable because different frequency components overlap and the original signal cannot be recovered correctly.
- However, bandpass sampling is a special and intentional use of undersampling for band-limited signals, where aliasing is controlled rather than avoided completely.
- The key requirement is that the aliased frequency bands must not overlap, allowing the original information to remain intact.
In summary,
undersampling is usually a source of error, but when carefully designed for narrowband signals, it becomes bandpass sampling—a practical and efficient technique used in real-world systems such as RF signal processing.
Suggested Further Reading
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Undersampling vs Bandpass Sampling Explained
Sampling is usually explained using the Nyquist rule. Sample at least 2× the highest frequency, but in practice, things are more interesting.
Sometimes we intentionally sample below Nyquist!
What Is Undersampling?
Undersampling happens when sampling rate is less than 2× the highest frequency
Result
Key Idea
Intuition
“Sampling too slow → information overlaps”
What Is Bandpass Sampling?
Bandpass sampling is a controlled form of undersampling.
Done intentionally!
Key Idea
If the signal is band-limited (not from 0 Hz)
You can sample below Nyquist without losing information
How Bandpass Sampling Works
Bandpass signals can be shifted (aliased) into baseband.
Concept
Key Conditions
Frequency Folding (Aliasing)
When sampling, frequencies fold into lower range.
Relationship
Alias Frequency = | Signal frequency - Closest sampling frequency Harmonic |
Meaning
MALMIJAL Example
then downsampling to 30Hz for intentional aliasing (frequency folding or shifted into baseband)
FFT of Noisy signal with 3000Hz sample rate (95 and 100Hz peaks)
FFT of intentional aliasing with 30Hz sample rate (5 and 10Hz peaks), almost same information as above
No information lost when bandpass filtering, showed without noise for clarity
Key Difference
Real-World Applications
RF Communication
Falias = | 960 - 12*80 | = 0MHz, | 950 - 12*80 | = 10MHz, | 940 - 12*80 | = 20MHz
Vibration Analysis
Spectrum Analysis
Key Takeaways
Conclusions
Undersampling normally causes aliasing and distortion because the sampling rate is lower than twice the highest frequency component.
In summary,
undersampling is usually a source of error, but when carefully designed for narrowband signals, it becomes bandpass sampling—a practical and efficient technique used in real-world systems such as RF signal processing.
Suggested Further Reading
##You may also be interested in these topics: