aifourier 2.1.1

AI-based Fourier Analysis using sinusoidal neural networks

AI-Based Fourier Analysis (aifourier)

“Machines can learn Fourier analysis.”

A Python library that approximates Fourier decomposition using a sinusoidal neural network.

Instead of explicitly computing Fourier integrals, this library learns the frequency components of a signal through optimization.

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✨ Features

• 🔊 Analyze audio signals (.wav, .mp3, .flac, .ogg)

• 🧠 Neural network with sinusoidal activation

• 📊 Extract:

  • Frequencies in Hz
  • Phase shift
  • Amplitude

• ⚡ Simple one-line API

• 📁 Output as Pandas DataFrame

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📦 Installation

pip install aifourier

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🚀 Usage

import aifourier as aif

df = aif.analyze("audio.mp3")

print(df.head())

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📊 Output

The result is a DataFrame containing:

Column	Description
Frequencies	Learned frequencies (Hz)
Phase shift	Phase of each component
Amplitudes	Contribution strength of each mode

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🧠 How It Works

The signal is approximated as:

y(t) ≈ Σ Aᵢ sin(ωᵢ t + φᵢ)

Where:

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

These parameters are learned by a neural network instead of computed analytically.

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⚙️ Parameters

aif.analyze(audio_path, max_modes=10000, epochs=256,use_phase_shift=True,learning_rate=0.00001,save_model=None,verbose=2,positive_freqs_only=True,abs_amplitudes=True)

• audio_path : Path to audio file
• max_modes : Number of sinusoidal components
• epochs : Training iterations (higher = better approximation)
• use_phase_shift : If this set to False, all phase shifts are set to zero.
• learning_rate : Learning rate of NN
• save_model : Path to save learned model
• verbose : Modes to show training behavior, which can be set to 0,1,2.
• positive_freqs_only : If this set to True, this will keep the positive frequencies and delete the negative ones.
• abs_amplitudes : If this set to True, all negative amplitudes will be positive-valued.

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📁 Example

See the examples/ folder for a complete demo:

cd examples
python example.py

This will:

• Analyze bird.mp3
• Generate frequency components
• Save results
• Plot the spectrum

The frequency spectrum of bird.mp3 is shown below:

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⚖️ Comparison with FFT

Method	Approach
FFT	Analytical, deterministic
aifourier	Learning-based, approximate

This project explores whether neural networks can discover Fourier structure from data.

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🚧 Limitations

• Approximation quality depends on training
• Slower than FFT
• Results may vary between runs

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💡 Future Ideas

• Signal reconstruction from learned parameters
• FFT comparison mode
• Real-time signal analysis (oscilloscope / radio)
• Complex-valued extensions

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👤 Author

Jovan, 2026

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📜 License

MIT License

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“What Fourier derives analytically, neural networks can approximate through learning.”