Overview
A low-pass filter smooths a signal by allowing frequencies below a cutoff to pass more strongly than frequencies above it. The exact behavior depends on filter type, order, and transition band.
CoreSource checked
Low-Pass Filter
Attenuates high-frequency signal components while preserving slower variations.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Beginner
- Family
- Filtering
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 5
- Code example
- Not ready
- Visualization
- Ready
- Aliases
- LPF
Core Concepts
signal samplesfilter kernellow-frequency retentionnoise smoothingfilteringsample windowsignal transformnoise handling
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n)
Space
O(1)
When to Use
- Use when desired signal content changes more slowly than the noise.
- Use before reducing sample rate when aliasing must be controlled.
When Not to Use
- Avoid when sharp transients or high-frequency details are important.
- Avoid when phase delay or latency would break the application.
What It Does
- Defines a cutoff between passband and stopband
- Suppresses rapid changes or high-frequency noise
- Outputs a smoother signal
Use Cases
- Noise reduction before analysis
- Anti-aliasing before downsampling
- Smoothing sensor measurements
Inputs
- Signal
- Cutoff frequency or smoothing factor
Outputs
- Filtered signal
Key Formulas (1)
Simple low-pass filter
y[i] = α · x[i] + (1 − α) · y[i − 1]
y[i] = alpha * x[i] + (1 - alpha) * y[i - 1]Smooths a signal by blending the new input with the previous output.
Pseudocode
- 1.Choose sample rate, cutoff, and filter design
- 2.Compute filter coefficients or state update parameters
- 3.For each sample, update the filter state
- 4.Emit the filtered sample
- 5.Handle startup and boundary behavior explicitly
Canonical Example
- Input
- signal with slow trend plus alternating high-frequency noise
- Output
- signal where the slow trend remains and the alternating noise is reduced
- Explanation
- The filter attenuates components above the cutoff frequency.
Implementation Notes
- Specify cutoff relative to the sampling rate.
- Choose FIR or IIR behavior based on phase, latency, and stability needs.
- Test with sine waves below and above the cutoff.
Common Pitfalls
- A cutoff chosen without the sampling rate is meaningless.
- Filter delay can shift features in time.
- Too aggressive smoothing can remove real events.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow a noisy signal becoming smoother after filtering.
Step 1 of 5: Choose sample rate, cutoff, and filter design
smoothed-waveformNotes
Low-pass filtering trades noise suppression for delay and loss of high-frequency detail.
Sources (1)
What each reference supports for this entry.
Discrete-Time Signal Processing
BookSignal-processing reference covering digital filter behavior and frequency-selective filtering.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Has variantsButterworth Filter
Signal Processing · Extended
Butterworth filters are often designed as maximally flat low-pass filters.
Compare with thisAlternative toHigh-Pass Filter
Signal Processing · Core
Low-pass filters preserve slow components, while high-pass filters preserve rapid changes.
Compare with thisRelationships
View full relationship pageAlternative toHigh-Pass Filter
Low-pass filters preserve slow components, while high-pass filters preserve rapid changes.
Conceptual neighborWindowing
Both require frequency-domain assumptions tied to sampling and signal preparation.
Related Algorithms
Tags
Signal ProcessingFilteringLow PassSmoothing