Overview
A Moving Average filter computes local averages across a sliding window, reducing short-term fluctuations while preserving slower trends.
FoundationSource checked
Moving Average
Smooths a sequence by replacing each value with an average over a nearby window.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Beginner
- Family
- Smoothing Filter
- Tier
- Foundation
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 5
- Code example
- Not ready
- Visualization
- Ready
- Aliases
- Rolling Average
Core Concepts
sliding windowlocal averagesmoothinglag
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 it for simple smoothing of time series or sampled signals.
- Use it when a small amount of lag is acceptable.
- Use cumulative sums for efficient fixed-width window averages.
When Not to Use
- Avoid it when sharp changes must be preserved.
- Avoid it when phase lag is unacceptable without compensation.
- Avoid it when outliers dominate the mean.
What It Does
- Smooths short-term variation
- Tracks local trend
Use Cases
- Time-series smoothing
- Noise reduction
- Simple trend indicators
Inputs
- Sequence of values
- Window size
Outputs
- Smoothed sequence
Key Formulas (1)
Moving average
averagei = ∑(x[i − k + 1] … x[i]) / k
average_i = sum(x[i - k + 1] ... x[i]) / kSmooths a signal by averaging a fixed-size local window.
Pseudocode
- 1.Choose a window size
- 2.Keep a running sum of values in the window
- 3.Divide the sum by the window length
- 4.Move the window one position
- 5.Update the running sum and repeat
Canonical Example
- Input
- samples = [1, 2, 3, 2, 1]
- Output
- transformed or filtered samples
- Explanation
- Moving Average: The algorithm reads local or frequency structure from the sample sequence.
Implementation Notes
- Specify centered, trailing, or leading window alignment.
- Use a running sum to update fixed-size windows in O(1) per sample.
- Decide how to handle incomplete windows at the edges.
Common Pitfalls
- Forgetting that larger windows increase smoothing and delay.
- Handling boundaries inconsistently.
- Using a mean when a median or robust filter is needed.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow a window moving over a line chart and smoothing the output.
Step 1 of 5: Choose a window size
sliding-averageNotes
Moving averages trade noise reduction for lag and blurred transitions.
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.
Alternative toExponential Moving Average
Signal Processing · Core
Moving average uses a fixed window, while EMA uses decaying weights.
Compare with thisAlternativesSavitzky-Golay Filter
Signal Processing · Extended
Savitzky-Golay smoothing preserves local polynomial shape better than a plain average.
Compare with thisRelationships
View full relationship pageAlternative toExponential Moving Average
Moving average uses a fixed window, while EMA uses decaying weights.
SpecializesLow-Pass Filter
A moving average is a simple low-pass smoothing filter.
Related Algorithms
Tags
Signal ProcessingFilteringSmoothing