Low-Pass Filter Effect

Explore how cutoff frequency, filter order, noise, and sample rate change sensor signal conditioning.

animation

sensing

actuation

signal-processing

filtering

sensors

noise-reduction

beginner

A beginner-first low-pass filter workbench with animated waveforms, frequency response, spectrum bars, cutoff guidance, and technical accuracy notes.

Animation Signal Filtering Sensor Noise Beginner First

Low-Pass Filter Effect

Watch a noisy sensor signal pass through a low-pass filter. The useful slow signal should survive, high-frequency noise should shrink, and the learner should notice the cost: lag and possible loss of real fast changes.

8.0 Hzcutoff frequency

-22 dBnoise attenuation

96%signal preserved

20 msapprox delay

TryLoad Temperature, place the 8.0 Hz Cutoff frequency between the 1.0 Hz signal and 50 Hz noise, then press Play and raise Filter order.

ObserveUse Spectrum to compare attenuation at 1.0 Hz and 50 Hz, then inspect Waveform for lag. Additional order makes the Response roll-off steeper but delays transitions.

ExplainComponents well below cutoff pass with little attenuation, while components above it are reduced according to the transfer function. Cascading filter stages sharpens that separation and accumulates phase shift.

Technical boundariesThe idealised response excludes analogue component tolerances, ADC quantisation, startup transients, nonlinear sensor response, time-varying noise, clipping, and implementation-specific group delay.

Colour keysensors identitycurrent / primaryreference / datasuccesscautionerror / failure

Goal

Choose a cutoff that removes high-frequency noise without flattening the real sensor behavior.

Try First

Use Temperature sensor, then lower the cutoff. Watch smoothing improve while response delay grows.

Watch

The waveform, spectrum bars, cutoff marker, and diagnosis update together from the same settings.

Why It Matters

Filtering before an ADC can reduce noise and aliasing, but a poor cutoff can hide real events.

1. Raw inputThe sensor includes useful signal plus unwanted fast variation.

2. CutoffThe cutoff marks the -3 dB boundary for a Butterworth-style response.

3. AttenuateComponents above cutoff are reduced by the filter response.

4. OutputThe filtered signal is smoother but may lag behind the input.

5. DecideCheck whether the signal is preserved, noise is reduced, and delay is acceptable.

Controls

Pick a sensor case, tune the filter, and compare time-domain and frequency-domain effects.

Scenarioslow sensor

Viewtime domain

Playbackmanual

Cutoff frequency 8.0 Hz

Set above the useful signal and below the unwanted noise when possible.

Filter order 2

Higher order gives steeper roll-off but can add delay and design complexity.

Signal frequency 1.0 Hz

The useful sensor motion you want to preserve.

Noise frequency 50 Hz

Fast interference from mains, motors, switching supplies, or vibration.

Noise level 45%

Higher noise makes the benefit of filtering easier to see.

Sample rate 200 Hz

Sampling must be high enough for the signal and any remaining noise.

Waveform View

The waveform view compares raw sensor input, filtered output, and the moving sample cursor.

Raw input

Reading: A low-pass filter keeps slow changes and reduces faster components.

Filter Diagnosis

The current filter should smooth noise while preserving the useful sensor signal.

ScenarioTemperature

Cutoff8.0 Hz

Order2

Signal gain96%

Noise gain8%

VerdictGood cutoff

Design Log

Cutoff Rule

For a first-order RC filter, fc = 1 / (2 pi R C).

Cutoff should sit above the useful signal band.

Response Rule

Butterworth magnitude: |H(f)| = 1 / sqrt(1 + (f/fc)^(2n)).

At f = fc, the gain is about 0.707, or -3 dB.

Delay Rule

More smoothing usually means more delay.

A filter that hides noise can also hide fast events.

Beginner Ramp

Low-pass: slow changes pass through more easily than fast changes.
Cutoff: the frequency where a Butterworth response is down about 3 dB.
Noise: unwanted variation that may be faster than the real sensor signal.
Lag: filtered output can respond later than the raw input.

Quick Reference

Choose cutoff above useful signal bandwidth, not below it.
Filter before the ADC when high-frequency analog noise could alias into the measurement.
Higher order gives a sharper transition band but is not automatically better.
Software filtering helps after sampling, but cannot undo aliasing already captured by the ADC.

Decision Pattern

Identify the useful signal frequency range.
Identify dominant noise frequencies.
Pick a cutoff between signal and noise when possible.
Check delay and step response.
Verify with real data from the sensor and installation.

Common Mistakes

Setting cutoff so low that real changes are flattened.
Thinking a moving average before sampling prevents analog aliasing.
Using a high-order filter without checking stability, delay, and implementation limits.
Reading a smoother graph as a more accurate measurement without calibration evidence.

Technical Accuracy Notes

The time trace uses cascaded EMA sections as a teaching approximation of low-pass smoothing.
The frequency-response chart uses the Butterworth magnitude formula shown above.
For a simple RC analog filter, tau = R C and fc = 1 / (2 pi tau).
At least sample above twice the highest frequency that remains after analog filtering; practical systems need margin.

Application Notes

Temperature and humidity sensors often need low cutoffs because the real world changes slowly.
Vibration sensing needs much higher bandwidth, so an aggressive low cutoff can destroy the signal.
Motor noise, power-line pickup, and switching supplies often require layout and shielding as well as filtering.

Practice 1

Select Temperature. Lower cutoff until the noise attenuation improves, then stop before delay becomes excessive.

Practice 2

Select Vibration. Raise signal frequency and notice why a low cutoff can remove real information.

Practice 3

Select Pressure step. Compare Waveform and Response views to explain smoothing versus response time.