Overview
Polyphase resampling avoids computing unused filter outputs when changing sample rates by rational factors.
ExtendedSource checked
Polyphase Resampling
Resamples a signal efficiently by splitting interpolation filters into phases.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Signal Processing
- Difficulty
- Advanced
- Family
- Resampling
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
rational resamplingpolyphase filterphase indexanti-aliasing
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n k)
Average
O(n k)
Worst
O(n k)
Space
O(k phases)
When to Use
- Use when filtering noisy signals needs rational resampling.
- Use when the input matches the assumptions behind resampling.
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
- Resamples a signal efficiently by splitting interpolation filters into phases
- Uses rational resampling and polyphase filter 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)
Rational rate change
outputrate = inputrate · L / M
output_rate = input_rate * L / MDescribes upsampling by L and downsampling by M.
Pseudocode
- 1.Prepare the inputs and state needed for Polyphase Resampling.
- 2.Apply the rational resampling step while the stopping condition has not been met.
- 3.Update intermediate state and discard invalid candidates.
- 4.Return filtered signal.
Canonical Example
- Input
- Polyphase Resampling input with a small representative case
- Output
- Filtered signal
- Explanation
- Polyphase Resampling applies rational resampling to produce filtered signal.
Implementation Notes
- Document sample rate, windowing, and normalization conventions.
- Keep the rational resampling step separate enough to test independently.
Common Pitfalls
- Boundary handling and normalization choices can change the interpretation of the result.
- Forgetting to check edge cases can make Polyphase Resampling look correct on only ideal inputs.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow the input signal beside the filtered, transformed, or reconstructed output.
Step 1 of 4: Prepare the inputs and state needed for Polyphase Resampling.
signal-processing-mechanismNotes
Polyphase Resampling should be used with the assumptions and tradeoffs of resampling 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 pageUsesFIR Filter
Polyphase resampling decomposes FIR filtering across sample phases.
Related Algorithms
Tags
Signal ProcessingResamplingFilteringPolyphase