Signal Processing Toolkit - Documentation!

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• Authors: Nikesh Bajaj, Jesús Requena Carrión

• Version: 0.0.9.4 | 01/01/2022

• Homepage : https://spkit.github.io

See also

Info

Version: 0.0.9.4 | Released on 01/01/2022

• Homepage spkit - https://spkit.github.io

• New Guide: - https://spkit.github.io/guide/

Getting started

• Links:
• Installation

Information Theory

• Information Theory for Real-Valued signals
  • Entropy of real-valued signal (~ IID)
    • View in Jupyter-Notebook
    • Shannan entropy
    • Rényi entropy (e.g. Collision Entropy)
    • Mutual Information & Joint Entropy
    • Conditional entropy
    • Cross entropy & Kullback–Leibler divergence
  • Entropy of real-valued signal (~ non-IID)
    • Spectral Entropy
    • Approximate Entropy
    • Sample Entropy
    • Singular Value Decomposition Entropy
    • Permutation Entropy
    • Dispersion Entropy
  • EEG Signal
    • View in Jupyter-Notebook
    • Single Channel
    • Multi-Channels (cross)

Dispersion Entropy (time-series, physiological signals)

• Dispersion Entropy
  • Backgorund
  • An Example
    • Important Note: Log base
  • Embedding diamension 4
  • Dispersion Entropy with sliding window
  • Dispersion Entropy multiscale
  • Mltiscale-refined Dispersion Entropy
  • View in Jupyter-Notebook for details

EEG Artifact Removal Algorithms

• ATAR - Automatic and Tunable Artifact Removal Algorithm for EEG
  • Notebook
    • View in Jupyter-Notebook
  • (1) Soft Thresholding (𝛽=0.1) - a quick example
  • (2) Linear Attenuation
  • (3) Elimination
  • Tuning 𝛽 with ‘soft’ : Controlling the aggressiveness
  • Tuning 𝛽 with ‘elim’
  • Tuning 𝛽 with ‘linAtten’
  • Other Settings
    • wavelet function
    • upper and lower bounds: \(k_1\) and \(k_2\)
    • IPR - Interpercentile range
    • constant threshold (θ=300), (not adaptive)
    • fixing threshold (θα=300), not using ipr method to adaptively change threshold
    • window length (5 sec)
• Blind Source Seperation - ICA Based Artifact Removal
  • Notebook
    • View in Jupyter-Notebook
  • A quick example
  • With smallar segment

Complex Continuous Wavelet Transform

• Complex Wavelets
  • Notebook
    • View in Jupyter-Notebook
  • A quick example to compare different wavelets
  • Gauss wavelet
    • Plot wavelet functions
    • With a range of scale parameters
    • Signal Analysis - EEG
    • Scalogram with default parameters
    • With a range of frequency and Q
    • With a plot of analysis wavelets
    • Speech
    • Audio
  • Morlet wavelet
  • Gabor wavelet
  • Poisson wavelet
    • #Type 1 (n)
    • #Type 2
    • #Type 3 (n)
  • Maxican wavelet
  • Shannon wavelet

Ramanujan Filter Banks for Period Estimation

• Ramanjum Filter Banks
  • Period estimation using RFB - (spkit version 0.0.9.4)
  • Single pattern with period of 10
  • Multiple pattern with periods of 3,7 and 10

Analysis and Sythesis Models

• Analysis and Synthesis Models
• DFT: Analysis and Synthesis
  • Analysis and Synthesis
  • Plot figures
  • Effect of windowing
  • No windowing
  • View in Jupyter-Notebook
• STFT: Analysis and Synthesis
  • Analysis and Synthesis
  • Plot figures:
  • View in Jupyter-Notebook
• FRFT: Fractional Fourier Transform
  • Analysis and Synthesis
  • Plot figures
  • View in Jupyter-Notebook-1
  • View in Jupyter-Notebook-2
• Sinasodal Model: Analysis and Synthesis
  • Analysis and Synthesis
  • Plots
  • Residual
  • Audio output
    • Original Audio
    • Reconstructed Audio
    • Residual Audio - hissing sound
  • View in Jupyter-Notebook-1
  • View in Jupyter-Notebook-2

DFT and STFT for Analysis and Sythesis of signals

#TODO

Franctional Fourier Transform

• Fractional Fourier Transform
  • View in Jupyter-Notebook
    • Fractional Fourier Transform
    • Fast Fractional Fourier Transform

Filtering

• Signal Filtering
  • Removing DC component (removing drift) - using IIR
  • Removing DC component (removing drift) - using Savitzky-Golay filter
  • Filtering frequency components - using IIR (butterworth) filter
  • Wavelet Filtering
  • Wavelet Filtering - on smaller windows

Wavelet Filtering

• Wavelet Filtering
  • Background
  • Example
  • View in Jupyter-Notebook for details and more examples

Independent Component Analysis

• Independent Component Analysis - ICA
  • View in Jupyter-Notebook

EEG Topographic Maps (Spatio-Temporal/Spectral)

• EEG Topographic Maps
  • Spatio-Temporal Map
  • Spatio-Spectral Map
  • Spatio-Spectro-Temporal Map

Machine Learning

• Machine Learning
  • New Updates
    • Decision Tree - View Notebooks
  • Logistic Regression
    • View more examples in Notebooks
    • Binary Class
    • Multi Class - with polynomial features
  • Naive Bayes
    • View more examples in Notebooks
  • Decision Trees
    • View more examples in Notebooks
    • Depth Analysis
    • Plottng tree while training

Basic-utilities

• Periodogram
• A quick stats of an array
• Compute statistical outliers

LFSR

• Link to pylfsr documentation
  • Example: 5 bit LFSR with x^5 + x^2 + 1
  • Check out full documentation of LFSR**

API DOc

• API docs
  • Entropy Functions
    • entropy()
    • mutual_Info()
    • dispersion_entropy()
    • dispersion_entropy_multiscale_refined()
  • Information Theory Module
    • Information Theory techniques
    • A_law()
    • Mu_law()
    • Quantize()
    • TD_Embed()
    • binSize_FD()
    • bin_width()
    • entropy()
    • entropy_approx()
    • entropy_cond()
    • entropy_cross()
    • entropy_joint()
    • entropy_kld()
    • entropy_permutation()
    • entropy_sample()
    • entropy_spectral()
    • entropy_svd()
    • mutual_Info()
    • plotJointEntropyXY()
    • quantize_FD()
  • Wavelet Analysis
    • ScalogramCWT()
  • Analysis & Synthesis Models
    • dft_analysis()
    • dft_synthesis()
    • stft_analysis()
    • stft_synthesis()
    • sineModel_analysis()
    • sineModel_synthesis()
    • frft()
    • ifrft()
    • ffrft()
    • iffrft()
    • RFB()
    • RFB_prange()
    • Create_Dictionary()
    • PeriodStrength()
    • RFB_example_1()
    • RFB_example_2()
    • filterDC()
    • filterDC_sGolay()
    • filter_X()
    • ATAR()
    • ATAR_1Ch()
    • ATAR_mCh()
    • ICA_filtering()
    • ICAremoveArtifact()
    • LR()
    • LogisticRegression()
    • NaiveBayes()
    • ClassificationTree()
    • RegressionTree()
  • List of all functions

ChangeLog

• ChangeLog

Index List

List

• Examples
• Signal Processing toolkit
• Signal Processing toolkit
• Analysis and Synthesis Models
• DFT: Analysis and Synthesis
• STFT: Analysis and Synthesis
• FRFT: Fractional Fourier Transform
• Sinasodal Model: Analysis and Synthesis
• API docs
• ATAR - Automatic and Tunable Artifact Removal Algorithm for EEG
• Periodogram
• A quick stats of an array
• Compute statistical outliers
• ChangeLog
• Contacts
• Complex Wavelets
• Dispersion Entropy
• EEG Topographic Maps
• Signal Filtering
• Fractional Fourier Transform
• Independent Component Analysis - ICA
• Blind Source Seperation - ICA Based Artifact Removal
• Signal Processing Toolkit - Documentation!
  • Links:
  • Installation
  • Information Theory for Real-Valued signals
  • Dispersion Entropy
  • ATAR - Automatic and Tunable Artifact Removal Algorithm for EEG
  • Blind Source Seperation - ICA Based Artifact Removal
  • Complex Wavelets
  • Ramanjum Filter Banks
  • Analysis and Synthesis Models
  • DFT: Analysis and Synthesis
  • STFT: Analysis and Synthesis
  • FRFT: Fractional Fourier Transform
  • Sinasodal Model: Analysis and Synthesis
  • Fractional Fourier Transform
  • Signal Filtering
  • Wavelet Filtering
  • Independent Component Analysis - ICA
  • EEG Topographic Maps
  • Machine Learning
  • Periodogram
  • A quick stats of an array
  • Compute statistical outliers
  • Link to pylfsr documentation
  • API docs
  • ChangeLog
  • Contacts
• Signal Processing ToolKit documentation!
  • Signal Processing toolkit
  • Examples
• Information Theory for Real-Valued signals
• Links:
• Installation
• Machine Learning
• Link to pylfsr documentation
• Ramanjum Filter Banks
• Sinasodal Model: Analysis and Synthesis Models
• Analysis and Synthesis Models
• Wavelet Filtering

Contacts

• Contacts