Adaptive & Blind Signal Processing Notebooks

Educational Jupyter notebooks for adaptive and blind signal processing. A minimal, clean implementation collection for educational demonstration and hands-on experimentation.

• Adaptive Signal Processing (LMS, ALE, ANC)
• Blind Source Separation (JADE, FastICA, SOBI)
• Designed for seminars, lectures, and hands-on practice.

Run notebooks directly in Google Colab via the badges below.
Repository: https://github.com/ogawa-tdu/dsp-adaptive-blind

Recommended Learning Path:
FND → ASP → (BE or BSS)

Choose BE for blind equalization problems (channel compensation),or BSS for source separation problems.

Quick Start

1. Open a notebook using the "Open in Colab" badge.
2. Run all cells from top to bottom.
3. Modify key parameters (e.g., SNR, step size, filter order, lag number) and observe how the results change.

No installation is required if you use Google Colab.

How to Experiment

These notebooks are designed for exploration.

• Change one parameter at a time and observe the effect.
• Try extreme values to understand failure cases.
• Compare time-domain and frequency-domain behavior.
• Ask: Why does this work? When does it fail?

Signal processing is best understood through controlled experimentation.

Suggested Exploration Themes

• Stability vs. convergence speed (LMS step size)
• Noise level vs. recoverability (SNR)
• Model order vs. performance
• Assumptions vs. reality (stationarity, independence, etc.)

Repository Structure

notebooks/  
├── ASP/  
│   ├── DSP_ASP_01_LMS.ipynb
│   ├── DSP_ASP_02_ALE.ipynb
│   ├── DSP_ASP_03_ANC.ipynb  
│   └── DSP_ASP_04_SysIdentification_Compare.ipynb  
├── BE/  
│   ├── DSP_BE_01_Sato_Algorithm.ipynb
│   └── DSP_BE_02_CMA.ipynb
├── BSS/  
│   ├── DSP_BSS_01_JADE.ipynb  
│   ├── DSP_BSS_02_FastICA.ipynb  
│   └── DSP_BSS_03_SOBI.ipynb
└── FND/
    ├── DSP_FND_01_Signal_and_Noise.ipynb
    └── DSP_FND_02_Wiener_filter.ipynb

Algorithmic Structure

Adaptive Signal Processing

• LMS : System identification
• ALE : Periodic signal enhancement
• ANC : Reference-based noise cancellation

Blind Source Separation

• JADE / FastICA : Higher-order statistics (ICA)
• SOBI : Second-order statistical BSS

Signal Processing Fundamentals (FND) Notebooks

Fundamental signal processing concepts and baselines for later algorithms (SNR, optimal filtering).

Signal & Noise (SNR demonstration)

Explores the relationship between SNR and signal clarity in both time and frequency domains.

Wiener filter

Demonstrates theoretical optimal noise reduction using the Wiener filter (MMSE). Explores frequency-domain gain design and practical limitations under real-world assumptions.

Adaptive Signal Processing (ASP) Notebooks

Online/recursive parameter estimation: update a filter from data to track changing systems and environments.

LMS

Adaptive filtering using LMS algorithm. Demonstrates convergence behavior and coefficient identification.

ALE

Noise reduction using Adaptive Line Enhancer (ALE). Demonstrates periodic component extraction from noisy signals.

ANC

Adaptive Noise Cancellation (ANC) using LMS. Implements a simplified feedforward ANC model without secondary path effects.

SysID: LMS vs NLMS vs APA vs RLS (comparison)

Compares adaptive filters for system identification under white/colored inputs. Highlights convergence speed, stability, and parameter sensitivity (e.g., RLS forgetting factor).

⚠️ Note on RLS: RLS is sensitive to λ and initialization; inappropriate settings may cause instability.

Blind Equalization (BE) Notebooks

Recover transmitted signals from unknown channels without training sequences.

Sato (4-PAM, real-valued)

Blind equalization using the Sato algorithm for multi-level PAM signals. Includes theoretical explanation, residual ISI monitoring, and pseudo-constellation (delay embedding) visualization.

CMA (4-PAM, real-valued)

Blind equalization using the Constant Modulus Algorithm (CMA). Demonstrates moment-based adaptation, residual ISI monitoring, and pseudo-constellation (delay embedding) visualization.

Blind Source Separation (BSS) Notebooks

Recover latent sources from mixtures using structural assumptions (e.g., independence, temporal diversity, low-rankness).

JADE

Blind source separation using fourth-order statistics (JADE). Demonstrates separation via joint diagonalization of cumulant matrices.

FastICA

Blind source separation using fixed-point ICA (FastICA). Demonstrates the effect of nonlinearity selection on separation performance.

SOBI

Blind source separation using second-order statistics (SOBI). Demonstrates the impact of lag design on separation quality.

Requirements

Tested on Google Colab (recommended)

• Python 3.9+
• NumPy
• SciPy
• Matplotlib
• librosa (optional, for audio demos)

Planned Additions

Signal Processing Fundamentals (FND)

• Ideal low-pass vs Wiener comparison
• Non-stationary noise example
• Causal FIR Wiener

Adaptive Signal Processing (ASP)

• Widely Linear LMS
• Kalman Filter
• Sparse algorithm

Blind Source Separation (BSS)

• Natural Gradient ICA
• Frequency domain ICA
• NMF based BSS
• Deep Learning based BSS
• Deep Unfolding based BSS

License

MIT License. Free for educational, research, and commercial use.