Sensors & Measurement · Study deck

Sampling and Anti-Alias Limits

Picture a spinning fan that appears to slow down when its speed actually rises.

Physics Phoebe is your guide for this deck.

sensordataprocessing

After studying this chapter

Learning objectives

You will be able to:

Explain: In: Properly Sampled, 500 Hz provides ten samples per cycle and an: Anti-alias filter at 180 Hz blocks higher-frequency content before conversion, allowing the FFT to match the mechanics.
Explain: The: Undersampled (Aliased) panel then uses an 80 Hz sample rate, whose 40 Hz Nyquist limit excludes the input; the samples reconstruct a false 30 Hz component from |80 − 50|.
Explain: In the sampling trace, a healthy motor turns with a real 12 Hz vibration while its drive adds a 38 Hz electrical ripple.
Decide when oversampling helps noise performance without pretending to fix aliasing.

Major section

Start With the Measurement Story

The sensor is not seeing the motion often enough, so the samples create a false pattern.

Analog-to-digital converter means a circuit that turns a voltage into a number; it is often shortened to ADC.
Firmware means the software stored on the device.
Feed in a known tone below and above the planned limit.

Major section

Predicting Frequency Aliases

The 50 SPS logger cannot represent the machine vibration assumed in this example.

The: Undersampled (Aliased) panel then uses an 80 Hz sample rate, whose 40 Hz Nyquist limit excludes the input; the samples reconstruct a false 30 Hz component from |80 − 50|.
In: Properly Sampled, 500 Hz provides ten samples per cycle and an: Anti-alias filter at 180 Hz blocks higher-frequency content before conversion, allowing the FFT to match the mechanics.
The final inequality, fmax < fsample / 2, is therefore an analogue-front-end contract, not a post-processing option.

Sampling a 50 Hz machine-vibration signal three ways: undersampling at 80 Hz aliases it to a false 30 Hz, while sampling at 500 Hz with an anti-alias filter reconstructs it faithfully.

Major section

Rescue a Motor Trace Before the ADC

In the sampling trace, a healthy motor turns with a real 12 Hz vibration while its drive adds a 38 Hz electrical ripple.

At this anti-alias boundary, if a logger takes only 50 samples each second, both motions can land on the same plotted frequency.
Once the ADC has confused them, a dashboard cannot tell which 12 Hz trace came from the shaft.
At 50 samples/s, Nyquist is $50/2=25\ \text{Hz}$ .

Major section

Rescue a Motor Trace Before the ADC (continued)

The ADC then takes spaced snapshots, and the digital analysis receives only those samples.

Raising the rate to 100 samples/s moves Nyquist to 50 Hz, so 38 Hz remains distinct.
A filter that strongly reduces input above 20 Hz offers another route when the 12 Hz motion is the only required result.
Without those two values, a 12 Hz peak cannot show whether the capture protected its frequency identity.

Major section

Rescue a Motor Trace Before the ADC (continued)

The anti-alias filter sits before the ADC because filtering after sampling cannot unfold a frequency that already has the wrong identity.

If sample spacing wanders, the frequency axis also becomes uncertain.
A timestamped capture can reveal dropped or late samples that a plain array of ADC values hides.
The ADC had already aliased 38 Hz, so attenuation does not restore the lost frequency identity.

Deck summary

Key takeaways

The sensor is not seeing the motion often enough, so the samples create a false pattern.

The 50 SPS logger cannot represent the machine vibration assumed in this example.
In the sampling trace, a healthy motor turns with a real 12 Hz vibration while its drive adds a 38 Hz electrical ripple.
The ADC then takes spaced snapshots, and the digital analysis receives only those samples.
The anti-alias filter sits before the ADC because filtering after sampling cannot unfold a frequency that already has the wrong identity.

Retrieval practice

Recall check 1 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q1Why must the sampling chain be checked before tuning a firmware filter?

AA firmware filter sets the original analog input bandwidth.

BCalibration always restores an aliased signal's true frequency.

CA dashboard can instruct the ADC to resample past analog data.

DA filter cannot restore a signal the ADC has already aliased.

Show answer

Answer: D Acquisition must represent the physical signal before later processing.

Retrieval practice

Recall check 2 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q2What does the Nyquist rule require to capture a signal without aliasing?

AThe sample rate must equal the highest frequency present.

BThe sample rate must be more than twice the highest frequency present in the signal.

CThe sample rate must be a whole-number multiple of the signal frequency.

DAny sample rate works as long as you average enough samples afterwards.

Show answer

Answer: B Below twice the highest frequency, fast components fold down and masquerade as slower ones.

Retrieval practice

Recall check 3 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q3Where should an anti-alias low-pass filter sit in a sensor chain?

AAt the cloud dashboard after digitization of samples.

BIn the analog path before the ADC samples the signal.

CInside the store for calibration coefficients.

DAfter conversion as a digital moving average.

Show answer

Answer: B Only an analog pre-sample filter can block out-of-band input.

Q4A 50 Hz vibration is sampled at 80 samples/s; which false frequency can appear?

A50 Hz

B80 Hz

C10 Hz

D30 Hz

Show answer

Answer: D The chapter example gives the fold as |80 − 50|.

Retrieval practice

Recall check 4 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q5You sample at 100 SPS and a 90 Hz interference tone is present. Where does it appear in the sampled data?

AAt 90 Hz because the ADC records the input tone at its original frequency.

BAt 45 Hz, from dividing the input tone frequency by two.

CAt 10 Hz, since the 90 Hz tone aliases below a 50 Hz Nyquist limit.

DAt no frequency because oversampling cancels the interference before conversion.

Show answer

Answer: C The 90 Hz tone folds down to a phantom 10 Hz component because |90 - 100 x round(0.9)| = 10 Hz.

Retrieval practice

Recall check 5 of 5

Physics Phoebe says: answer from memory, then check your reasoning.

Q6A team finds aliased interference in already-recorded sensor data and proposes a stronger digital low-pass filter to remove it. Why will this fail?

ADigital filters cannot attenuate any frequencies, only analog ones can.

BThe filter would work fine; the team simply chose the wrong cutoff.

CAfter sampling, the aliased component is indistinguishable from a genuine low-frequency signal.

DAliased components are always above the Nyquist frequency, where digital filters cannot reach.

Show answer

Answer: C Aliasing is irreversible once sampled; prevention has to happen in analog, before conversion.

Print reference

Answers 1 of 2

Answer key.

D · Acquisition must represent the physical signal before later processing.
B · Below twice the highest frequency, fast components fold down and masquerade as slower ones.
B · Only an analog pre-sample filter can block out-of-band input.
D · The chapter example gives the fold as |80 − 50|.
C · The 90 Hz tone folds down to a phantom 10 Hz component because |90 - 100 x round(0.9)| = 10 Hz.

Print reference

Answers 2 of 2

Answer key.

C · Aliasing is irreversible once sampled; prevention has to happen in analog, before conversion.