Py1DTDF

This Python package provides a comprehensive set of standard, fractal, nonlinear, and information-theoretic time-domain features for 1-D signals. The features are computed using an adjustable sliding window and overlap mechanism, allowing flexibility in analyzing different segments of a signal.Hence the name 1DTDF : 1-Dimensional Time-Domain Features.

Features

1. Standard Time-Domain Features

These features capture the statistical and structural properties of the signal over time.

• Mean: Measures the central tendency of the signal (Wikipedia).
• Standard Deviation: Measures the variability of the signal (Wikipedia).
• RMS (Root Mean Square): Measures the magnitude of the signal (Wikipedia).
• Skewness: Measures the asymmetry of the signal distribution (Wikipedia).
• Kurtosis: Measures the "tailedness" of the signal distribution (Wikipedia).
• Zero-Crossing Rate: Measures how often the signal crosses zero (Wikipedia).
• Maximum Value: Returns the maximum value in the window (Wikipedia).
• Minimum Value: Returns the minimum value in the window (Wikipedia).
• Peak-to-Peak: Measures the range between maximum and minimum values (Wikipedia).
• Variance: Measures the variability of the signal (Wikipedia).
• IQR (Interquartile Range): Measures the spread of the middle 50% of the data (Wikipedia).
• Number of Peaks: Returns the number of peaks in the window (Wikipedia).
• Signal Line Length: Measures the cumulative sum of absolute differences in the signal (Wikipedia).
• Crest Factor: Ratio of the peak value to the RMS value (Wikipedia).
• Shape Factor: Ratio of the RMS value to the mean absolute value (Wikipedia).
• Impulse Factor: Ratio of the peak value to the mean absolute value (Wikipedia).
• Signal Range: Difference between the maximum and minimum values (Wikipedia).
• Mean Crossing Rate: Measures how often the signal crosses its mean value (Wikipedia).
• Signal Variability: Standard deviation divided by the square root of the signal length (Wikipedia).
• Peak Amplitude: Returns the peak value of the signal (Wikipedia).
• Energy: Sum of squared values in the signal (Wikipedia).
• Median: Returns the median value of the signal (Wikipedia).
• Root Sum of Squares (RSS): Square root of the sum of squared values (Wikipedia).
• DASDV: Measures the variability of differences between consecutive points (IEEE).
• Range Ratio: Ratio of the range (max - min) to the standard deviation (Wikipedia).

2. Fractal Features

These features describe the complexity and self-similarity of the signal.

• Higuchi Fractal Dimension: Measures complexity using Higuchi's algorithm (Scientific Article).
• Hurst Exponent: Measures the long-term memory of the signal (Wikipedia).
• Lyapunov Exponent: Indicates chaos in the signal by measuring sensitivity to initial conditions (Wikipedia).
• Katz Fractal Dimension: Measures signal complexity using Katz's method (IEEE).
• Petrosian Fractal Dimension: Measures complexity by detecting changes in signal direction (IEEE).
• Box-Counting Fractal Dimension: Uses the box-counting method to estimate fractal dimension (Wikipedia).
• Correlation Dimension: Estimates the fractal dimension using the correlation integral (Wikipedia).

3. Complexity and Nonlinear Features

These features capture the irregularity, randomness, or chaotic nature of the signal.

• Approximate Entropy: Measures the complexity and unpredictability of the signal (Wikipedia).
• Sample Entropy: A more robust version of Approximate Entropy (Wikipedia).
• Shannon Entropy: Measures the uncertainty or randomness of the signal (Wikipedia).
• Lempel-Ziv Complexity: Measures the number of distinct patterns in the signal (Wikipedia).
• Permutation Entropy: Evaluates the complexity by analyzing the order of neighboring values (Wikipedia).
• Largest Lyapunov Exponent: Quantifies the divergence of nearby trajectories, indicating chaos (Wikipedia).
• Mobility: Measures the rate of change in the variance of the signal (Wikipedia).

4. Information-Theoretic Features

These features quantify the information content and uncertainty in the signal.

• Entropy: Shannon entropy of the signal (Wikipedia).
• Mutual Information: Measures the shared information between two parts of the signal (Wikipedia).
• Symbolic Dynamics Entropy: Measures randomness in symbolic transitions (Wikipedia).
• Conditional Entropy: The entropy of the signal conditioned on its past values (Wikipedia).

5. Statistical Moments and Distribution-Based Features

These features capture statistical properties of the signal distribution.

• Higher-Order Moments: Measures higher-order statistical moments (up to 6th order) (Wikipedia).
• Percentiles: Returns a specific percentile of the signal (Wikipedia).
• L-Moments: Linear combinations of order statistics to describe the shape of the distribution (Wikipedia).
• Quantile Range: Measures the spread between upper and lower percentiles (Wikipedia).
• Autoregressive Coefficients: Coefficients from an autoregressive model fitted to the signal (Wikipedia).

6. Geometric and Recurrence-Based Features

These features analyze the geometric structure of the signal trajectory and its recurrence.

• Recurrence Quantification: Measures the recurrence patterns of the signal (Wikipedia).
• Attractor Reconstruction: Reconstructs the attractor of the signal in phase space (Wikipedia).
• Mean Crossing Rate: Measures how often the signal crosses its mean value (Wikipedia).
• Max Slope: Measures the steepest slope between consecutive points (Wikipedia).

Installation

To install the package, run:

pip install py1dtdf

Usage

The software is licensed under the MIT License. Please see LICENSE file for more details.

import numpy as np
from py1dtdf import all_features

# Example signal
signal = np.sin(np.linspace(0, 10, 1000))  # Sine wave signal

# Set window size and overlap
window_size = 200
overlap = 100

# Compute all features for the signal
features = all_features(signal, window_size, overlap)

# Print all features
for feature_name, feature_values in features.items():
    print(f"{feature_name}: {feature_values}")