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.
✨ 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
📦 Installation
pip install aifourier
🚀 Usage
import aifourier as aif
df = aif.analyze(
"audio.mp3",
optimizer="adam"
)
print(df.head())
📊 Output
The returned DataFrame contains:
| Column | Description |
|---|---|
| Frequencies | Learned frequencies (Hz) |
| Phase shift | Learned phase shifts |
| Amplitudes | Learned amplitudes |
🧠 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.
⚙️ 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
)
| Parameter | Description |
|---|---|
audio_path |
Audio file path |
max_modes |
Maximum number of sinusoidal modes |
epochs |
Number of training epochs |
use_phase_shift |
Learn phase shifts |
learning_rate |
Optimizer learning rate |
save_model |
Save trained model |
verbose |
Training verbosity (0, 1, 2) |
positive_freqs_only |
Keep only positive frequencies |
abs_amplitudes |
Return absolute amplitudes |
optimizer |
Training optimizer |
show_spectrum |
Show spectrum plot preview |
save_spectrum |
Save spectrum plot figure to desired folder path |
📁 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.
🌊 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.
💡 Future Ideas
- Audio reconstruction
- FFT comparison utilities
- Real-time microphone analysis
- Radio signal analysis
- Oscilloscope support
- Complex-valued SinusoidalNN
👤 Author
Jovan
2026
📜 License
MIT License
"What Fourier derives analytically, Sinusoidal Neural Networks can approximate through learning."
1 maintainer
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