Overview
Overlap-Add splits a signal into blocks, processes each block, and adds overlapping output regions to produce a continuous result.
ExtendedSource checked
Overlap-Add
Reconstructs or filters long signals by summing overlapping processed blocks.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Intermediate
- Family
- Block Signal Processing
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 2
- Code example
- Ready
- Visualization
- Ready
Core Concepts
block processingoverlap regionsample summationwindowing
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n log block_size)
Worst
O(n log block_size)
Space
O(block_size)
When to Use
- Use when long signals must be processed in manageable blocks.
- Use when fFT convolution is a central requirement.
When Not to Use
- Avoid when block boundary latency or artifacts are unacceptable.
- Avoid when the sampling rate, window size, or stationarity assumptions do not hold.
What It Does
- Splits a signal into blocks
- Processes blocks independently
- Adds overlapping output samples
Use Cases
- FFT convolution
- Audio block processing
- STFT reconstruction
Inputs
- Signal blocks
- Window or filter
- Hop size
Outputs
- Reconstructed or filtered signal
Key Formulas (1)
Overlap sum
output[n] = ∑(blocki[n − offseti])
output[n] = sum(block_i[n - offset_i])Adds every processed block contribution that covers an output sample.
Pseudocode
- 1.Split the input into overlapping or padded blocks
- 2.Process each block
- 3.Place each processed block at its output offset
- 4.Add samples in overlapping regions
Canonical Example
- Input
- blocks = [0..3] and [2..5]
- Output
- overlap samples are summed
- Explanation
- The method combines block outputs into one continuous sequence.
Implementation Notes
- Verify perfect reconstruction with an identity processing pass.
- Plot or inspect both the original and processed signal for small test cases.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Using incompatible window and hop sizes can create amplitude modulation.
- Boundary handling and phase response can change the result in visible or audible ways.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow processed blocks laid over each other and summed into one continuous waveform.
Step 1 of 4: Split the input into overlapping or padded blocks
signal-transformNotes
Window and hop choices determine whether reconstruction is smooth.
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 toOverlap-Save
Both perform block convolution with different boundary handling.
Related Algorithms
Tags
Signal ProcessingFilteringTime FrequencyAudio Processing