Overview
The Least Mean Squares adaptive filter updates weights in the direction that reduces error between desired and predicted output.
CoreSource checked
LMS Adaptive Filter
Adapts filter weights to minimize the current squared error.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Intermediate
- Family
- Adaptive Filter
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
- Aliases
- Least Mean Squares Filter
Core Concepts
adaptive weighterror signalgradient estimatestep size
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 adaptive weight.
- Use when the input matches the assumptions behind adaptive Filter.
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
- Adapts filter weights to minimize the current squared error
- Uses adaptive weight and error signal 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)
LMS update
wnext = w + μ · e[n] · x[n]
w_next = w + mu * e[n] * x[n]Adapts filter weights using the current error.
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
- LMS Adaptive Filter
- Output
- Filtered signal
- Explanation
- LMS Adaptive Filter applies adaptive weight to produce filtered signal.
Implementation Notes
- Document sample rate, windowing, and normalization conventions.
- Keep the adaptive weight 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
LMS Adaptive Filter should be used with the assumptions and tradeoffs of adaptive Filter in mind.
Sources (1)
What each reference supports for this entry.
Adaptive Filter Theory
BookReference text for LMS and adaptive filtering methods.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageVariant ofFIR Filter
LMS commonly adapts FIR filter coefficients from an error signal.
Related Algorithms
Tags
Signal ProcessingAdaptive FilterFilteringEstimation