SpecializedSource checked

Phase Vocoder

Changes time scale or pitch by manipulating short-time Fourier transform frames.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Signal Processing
Difficulty: Advanced
Family: Time-Frequency Processing
Tier: Specialized
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 2
Code example: Ready
Visualization: Ready

Overview

A Phase Vocoder analyzes overlapping spectral frames, adjusts their timing or frequency interpretation, and reconstructs a signal with coherent phase.

Core Concepts

STFT framephase advancetime stretchingoverlap-add

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n log w)

Average

O(frames * w log w)

Worst

O(frames * w log w)

Space

O(w)

When to Use

Use when audio duration or pitch needs to change without simply changing playback speed.
Use when time stretching audio is a central requirement.

When Not to Use

Avoid when transient sharpness is more important than smooth spectral transformation.
Avoid when the sampling rate, window size, or stationarity assumptions do not hold.

What It Does

Analyzes overlapping spectral frames
Tracks phase changes
Resynthesizes with modified timing or pitch

Use Cases

Time stretching audio
Pitch shifting
Spectral audio effects

Inputs

Audio signal
Window size
Hop size
Stretch or pitch factor

Outputs

Modified audio signal

Key Formulas (1)

Phase advance

phase_expected = 2·π·bin·hop_size/fft_size

phase_expected = 2*pi*bin*hop_size/fft_size

Predicts how much phase should advance between adjacent frames.

Pseudocode

1.Compute STFT frames
2.Measure magnitude and phase for each bin
3.Adjust phase increments for the new timing
4.Reconstruct frames with inverse transforms
5.Overlap-add the frames

Canonical Example

Input: audio = 1 second tone, stretch = 2
Output: output = 2 second tone at similar pitch
Explanation: The vocoder spaces frames farther apart while preserving phase continuity.

Implementation Notes

Handle transients separately if percussive audio sounds smeared.
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

Ignoring expected phase advance causes phase drift between frames.
Boundary handling and phase response can change the result in visible or audible ways.
Not defining boundary, empty, or degenerate inputs before implementation.