Overview
A notch filter is useful for removing a known interference frequency, such as hum, without broadly smoothing the signal.
CoreSource checked
Notch Filter
Suppresses a narrow frequency band while leaving nearby frequencies mostly intact.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Intermediate
- Family
- Filter Design
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
stop bandcenter frequencyquality factorfrequency rejection
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(k)
Average
O(n k)
Worst
O(n k)
Space
O(k)
When to Use
- Use when filtering noisy signals needs stop band.
- Use when the input matches the assumptions behind filter Design.
When Not to Use
- Avoid when sampling rate, phase, or boundary assumptions are unknown.
- Avoid when a simpler algorithm gives the required result with less setup.
What It Does
- Suppresses a narrow frequency band while leaving nearby frequencies mostly intact
- Uses stop band and center frequency to guide the work.
- Produces filtered signal.
Use Cases
- Filtering noisy signals
- Spectral analysis
- Audio and sensor processing
Inputs
- Sampled signal
- Filter or transform parameters
Outputs
- Filtered signal
- Spectrum or feature representation
Key Formulas (1)
Notch distance
attenuate when |frequency − center| < bandwidth / 2
attenuate when |frequency - center| < bandwidth / 2Defines the narrow rejected region around the target frequency.
Pseudocode
- 1.Validate sampling rate, window, boundary, and parameter choices
- 2.Prepare the signal state, coefficients, or transform workspace
- 3.Apply the filter, transform, or measurement rule to each sample or frame
- 4.Handle boundaries and normalization consistently
- 5.Return the filtered signal, coefficients, or feature values
Canonical Example
- Input
- Notch Filter
- Output
- Filtered signal
- Explanation
- Notch Filter applies stop band to produce filtered signal.
Implementation Notes
- Document sample rate, windowing, and normalization conventions.
- Keep the stop band step separate enough to test independently.
- Keep sampling rate, window size, latency, and boundary conventions explicit in tests.
Common Pitfalls
- Boundary handling and normalization choices can change the interpretation of the result.
- Test edge cases, not only clean examples.
- Ignoring sampling rate, boundary handling, or phase behavior can make the output misleading.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow the input signal beside the filtered, transformed, or reconstructed output.
Step 1 of 5: Validate sampling rate, window, boundary, and parameter choices
signal-processing-mechanismNotes
Notch Filter should be used with the assumptions and tradeoffs of filter Design in mind.
Sources (1)
What each reference supports for this entry.
Discrete-Time Signal Processing
BookSignal-processing reference for digital filters, convolution, spectral analysis, windows, resampling, and transform-based methods.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toBand-Pass Filter
A notch filter rejects a narrow band, while a band-pass filter keeps one.
Related Algorithms
Tags
Signal ProcessingFilter DesignFrequency DomainFiltering