Wavelet Audio Analysis

A comprehensive Nim implementation of Discrete Wavelet Transform (DWT) for audio signal processing and analysis.

Features

• Complete DWT Implementation: Forward and inverse transforms with multiple wavelet families
• Audio Processing: WAV file reading/writing, windowing, and preprocessing
• Multiple Wavelets: Haar, Daubechies (db4, db8), Biorthogonal wavelets
• Analysis Tools: Energy analysis, frequency decomposition, denoising
• High Performance: Optimized algorithms with efficient memory usage
• Comprehensive Tests: Unit tests and benchmarks included

Wavelet Families Supported

• Haar: Simplest wavelet, good for signals with sharp transitions
• Daubechies: Orthogonal wavelets with various orders (db4, db8)
• Biorthogonal: Symmetric wavelets good for image/audio processing

Installation

nimble install

Usage

Basic DWT Example

import wavelet_audio

# Create a test signal
let signal = @[1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0]

# Perform DWT
let dwt = newDWT(WaveletType.Haar)
let (coeffs, lengths) = dwt.forward(signal)

# Reconstruct signal
let reconstructed = dwt.inverse(coeffs, lengths)

Audio Analysis Example

import wavelet_audio/audio

# Load audio file
let audio = loadWAV("input.wav")

# Analyze with DWT
let analyzer = newAudioAnalyzer(WaveletType.Daubechies4)
let analysis = analyzer.analyze(audio.samples, levels = 5)

# Get frequency band energies
echo "Energy distribution: ", analysis.energyDistribution

API Reference

Core DWT Classes

• DWT: Main wavelet transform class
• WaveletType: Enumeration of supported wavelets
• AudioAnalyzer: High-level audio analysis interface

Key Methods

• forward(signal): Perform forward DWT
• inverse(coeffs, lengths): Perform inverse DWT
• analyze(samples, levels): Analyze audio with multi-level DWT
• denoise(signal, threshold): Remove noise using wavelet thresholding

Building and Testing

# Run tests
nimble test

# Build release version
nim c -d:release src/wavelet_audio.nim

# Generate documentation
nimble docs

Performance

The implementation is optimized for performance with: - In-place operations where possible - Efficient memory management - SIMD-friendly algorithms - Benchmark suite included

Applications

• Audio denoising
• Feature extraction for music analysis
• Signal compression
• Time-frequency analysis
• Audio classification preprocessing

License

MIT License - see LICENSE file for details.

Contributing

Contributions welcome!