aifourier

AI-Based Fourier Analysis (aifourier)

"Machines can learn Fourier analysis."

aifourier is a Python library for AI-based Fourier analysis of audio signals, powered by Sinusoidal Neural Networks (SNN).

SinusoidalNN repo link (made by Jovan also): https://github.com/jovan-AIcoder/SinusoidalNN

Built on top of the SinusoidalNN python package framework, aifourier learns the frequency components of an audio signal through optimization instead of explicitly computing Fourier integrals.

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✨ Features

• 🔊 Analyze audio files (.wav, .mp3, .flac, .ogg)
• 🌊 Built on top of SinusoidalNN
• 🧠 Neural Fourier decomposition via optimization
• 📊 Extract:
  • Frequencies (Hz)
  • Phase shifts
  • Amplitudes
• ⚙️ Multiple optimizers
  • SGD
  • RMSprop
  • Adam
  • AdamW
  • Adagrad
  • Adadelta
  • Adamax
  • Nadam
  • Ftrl
• 📈 Training MAE monitoring
• ➕ Optional positive-frequency filtering
• ➕ Optional absolute amplitudes
• 💾 Save trained neural models
• 📁 Pandas DataFrame output
• ⚡ Simple one-line API

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📦 Installation

pip install aifourier

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🚀 Usage

import aifourier as aif

df = aif.analyze(
    "audio.mp3",
    optimizer="adam"
)

print(df.head())

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📊 Output

The returned DataFrame contains:

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🧠 How It Works

Instead of evaluating Fourier coefficients analytically,

y(t) ≈ Σ Aᵢ sin(ωᵢ t + φᵢ)

Where:

• Aᵢ = amplitude
• ωᵢ = angular frequency
• φᵢ = phase shift

these parameters are learned directly from data using a Sinusoidal Neural Network.

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⚙️ Parameters

aif.analyze(
    audio_path,
    max_modes=10000,
    epochs=256,
    use_phase_shift=True,
    learning_rate=1e-5,
    save_model=None,
    verbose=2,
    positive_freqs_only=True,
    abs_amplitudes=True,
    optimizer="adam",
    show_spectrum=False,
    save_spectrum=None
)

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📁 Example

See the examples/ folder:

cd examples
python example.py

Example workflow:

• Analyze bird.mp3
• Learn sinusoidal spectrum
• Export frequency table
• Plot the learned spectrum

The learned spectrum is shown below.

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🌊 Relationship with SinusoidalNN

SinusoidalNN
        │
        ▼
   aifourier

SinusoidalNN provides the neural network engine.

aifourier provides an easy-to-use interface for AI-based Fourier analysis of audio signals.

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💡 Future Ideas

• Audio reconstruction
• FFT comparison utilities
• Real-time microphone analysis
• Radio signal analysis
• Oscilloscope support
• Complex-valued SinusoidalNN

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👤 Author

Jovan

2026

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📜 License

MIT License

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"What Fourier derives analytically, Sinusoidal Neural Networks can approximate through learning."