Stochastic & Spectral Analysis of Encoded Video Signals

Instituto Militar de Engenharia — IME
Field: Statistical Signal Processing & Stochastic Systems
Standards Investigated: Digital video frame streams encoded under H.263 and MPEG-4

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🎯 Project Overview

Rigorous stochastic and spectral characterization of digital video transmission streams (frame size in bits over discrete time series), investigating:

1. Descriptive Statistics & Higher-Order Moments: Computation of Sample Mean ($\mu$), Variance ($\sigma^2$), Standard Deviation ($\sigma$), Mean Squared Value (MSV), and Root Mean Square (RMS).
2. Empirical Distribution & Normality Testing: Histogram generation with theoretical Gaussian / Normal density overlays.
3. Correlation Analysis: One-sided normalized Autocorrelation Functions (ACF) and Cross-Correlation Functions (CCF) across discrete positive lags ($k \ge 0$).
4. Covariance & Signal Decorrelation: Channel covariance matrix formulation, scatter visualization, and linear decorrelation transforms.
5. Power Spectral Density (PSD): Frequency-domain PSD estimation (dB) via Fast Fourier Transform (FFT / Periodogram) with noise chromaticity categorization (white vs. pink/brown noise).

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📂 Modular Architecture

modelos-tr3/
├── dados/                               # Raw time-series text files (.txt) containing frame bit sizes
├── resultados/                          # Automatically generated plots and numerical metrics
│   ├── passo1_sinais_e_histogramas/     # Discrete time-series plots x(n) and Gaussian-fitted histograms
│   ├── passo2_valores_esperados/        # Consolidated statistical summary report (estatisticas.txt)
│   ├── passo3_facs/                     # Autocorrelation (ACF) and cross-correlation (CCF) curves
│   ├── passo4_descorrelacao/            # Covariance matrices, scatter plots, and decorrelation transforms
│   └── passo6_7_dep_e_espectro/         # Power Spectral Density (PSD in dB) and frequency spectra
├── passo1_2_sinais_e_momentos.py        # Statistical moments and empirical distribution module
├── passo3_facs.py                       # Autocorrelation and cross-correlation module
├── passo4_descorrelacao.py              # Covariance matrix and decorrelation module
├── passo6_7_dep_e_espectro.py           # Spectral analysis and noise classification module
├── executar_tudo.py                     # Automated end-to-end processing pipeline
└── requirements.txt                     # Dependencies (numpy, scipy, matplotlib)

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📐 Mathematical Formulation

• Sample Autocorrelation Function (ACF): $$R_{xx}[k] = \frac{1}{N - k} \sum_{n=0}^{N-k-1} (x[n] - \mu_x)(x[n+k] - \mu_x)$$

• Power Spectral Density (Wiener–Khinchin Theorem): $$S_{xx}(f) = \mathcal{F}{ R_{xx}[k] } = \sum_{k=-\infty}^{\infty} R_{xx}[k] e^{-j 2 \pi f k}$$

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🚀 Execution & Quick Start

1. Install Python dependencies:

pip install -r requirements.txt

2. Place raw time-series data files in dados/.

3. Execute the automated analysis pipeline:

python executar_tudo.py

All high-resolution figures and statistical tables will be automatically exported to resultados/.

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👥 Author

• João Victor Pariz (@VPariz) — Electronics Engineering, Military Institute of Engineering (IME).