Computing Signal Correlation Dimension

Computing signal correlation dimension is a fundamental concept in signal analysis. The correlation dimension quantifies the amount of correlated information within a signal, serving as a metric to evaluate signal complexity and information content. Various computational approaches exist, including statistical-based methods and information-theoretic techniques. Common implementation involves using the Grassberger-Procaccia algorithm, which calculates the correlation integral C(r) by counting point pairs within distance r in the reconstructed phase space. The dimension is then derived from the slope of log C(r) versus log r plot. In MATLAB, this can be implemented using functions like corrdim() from the Chaos Toolbox or custom code involving phase space reconstruction via time-delay embedding. Key algorithmic steps include: 1. Phase space reconstruction using time-delay embedding parameters (τ, m) 2. Computation of correlation sum for varying distance thresholds 3. Linear regression on logarithmic scales to extract the scaling exponent By computing signal correlation dimension, we gain deeper insights into signal characteristics, enabling applications in signal processing and communication systems such as noise reduction, feature extraction, and system identification. The study and computation of correlation dimension therefore hold significant importance for advancing signal analysis techniques and their practical implementations.