LZ Complexity Reflects the Pattern Growth Rate in Time Series Analysis

As mentioned in the text: LZ complexity quantifies the rate of new pattern emergence relative to the increasing length of a time series. To computationally analyze complexity in continuous signals, digital discretization becomes necessary, a condition met by preprocessed heart sound signals. The separation of heart sound signals requires the following implementation steps:

1. Signal Discretization: Convert continuous analog signals into discrete digital sequences using sampling techniques (typically employing analog-to-digital conversion with specified sampling rates and bit depths) for computer processing.

2. LZ Complexity Calculation: Implement the Lempel-Ziv complexity algorithm to compute pattern diversity growth rates. The algorithm involves scanning the discrete sequence while maintaining a vocabulary of encountered patterns, incrementing the complexity counter whenever new subsequences are identified.

3. Heart Sound Preprocessing: Apply signal conditioning techniques including filtering (bandpass filtering 20-150 Hz for heart sounds), normalization, and noise reduction to meet computational requirements for reliable complexity analysis.

4. Signal Separation: Utilize computed complexity metrics as features for segmenting heart sounds into components (S1, S2, murmurs) through pattern recognition algorithms or threshold-based classification methods.

These steps enable effective computational analysis and separation of heart sound signals, facilitating deeper understanding of complexity characteristics in continuous physiological signals.