Hands-on Signal Analysis with Python: An Introduction

Preface
	For Whom This Book Is
	References
Contents
1 Introduction
	1.1 Signal Processing
		1.1.1 Typical Workflow
	1.2 Conventions and Mathematical Basics
		1.2.1 Notation
		1.2.2 Mathematical Basics
		1.2.3 Discrete Signals
	1.3 Accompanying Material
	1.4 Exercises
2 Python
	2.1 Getting Started
		2.1.1 Distributions and Packages
		2.1.2 Installation of Python
		2.1.3 Python Resources
		2.1.4 A Simple Python Program
	2.2 Elements of Scientific Python Programming
		2.2.1 Python Datatypes
		2.2.2 Indexing and Slicing
		2.2.3 Numpy Vectors and Arrays
		2.2.4 Pandas DataFrames
		2.2.5 Python Documentation
		2.2.6 Functions, Modules, and Packages
	2.3 IPython/Jupyter—An Interactive Programming Environment
		2.3.1 Overview
		2.3.2 First Session with the Qt Console
		2.3.3 Personalizing IPython/Jupyter
	2.4 Workflow for Python Programming
		2.4.1 Program Design
		2.4.2 Converting Interactive Commands into a Python Program
	2.5 Programming Tips
		2.5.1 General Programming Tips
		2.5.2 Python Tips
		2.5.3 IPython/Jupyter Tips
	2.6 Python Alternatives
	2.7 Exercises
	Reference
3 Data Input
	3.1 Text
		3.1.1 Visual Inspection
		3.1.2 Reading ASCII-Data
		3.1.3 Regular Expressions
	3.2 Excel
	3.3 Matlab
	3.4 Binary Data
		3.4.1 NPZ Format
		3.4.2 Structured Arrays
	3.5 Images
	3.6 Videos
	3.7 Sound
	3.8 Zipped Archives on the WWW
	3.9 Other Formats
	3.10 Exercises
4 Data Display
	4.1 Introductory Example
	4.2 Plotting in Python
		4.2.1 Functional and Object-Oriented Approaches
		4.2.2 Interactive Plots
	4.3 Saving a Figure
	4.4 Preparing Figures for Presentation
		4.4.1 General Considerations
		4.4.2 Modifying SVG Figures
	4.5 Displaying Data Sets
		4.5.1 Plots of Data with One Variable
		4.5.2 Plots of Data with Two or More Variables
	4.6 Exercises
5 Data Filtering
	5.1 Transfer Functions
	5.2 Filter Types
		5.2.1 Linear Time Invariant (LTI) Filters
		5.2.2 Finite Impulse Response (FIR) Filters
		5.2.3 Infinite Impulse Response (IIR) Filters
		5.2.4 Morphological Filters
	5.3 Filter Characteristics
		5.3.1 Impulse- and Step-Response
		5.3.2 Frequency Response
		5.3.3 Artifacts in Causal Filters, and Non-causal Filters
	5.4 Applications
		5.4.1 Savitzky–Golay Filter
		5.4.2 Smoothing of Regularly Sampled Data
		5.4.3 Differentiation
		5.4.4 Integration
	5.5 Smoothing of Irregularly Sampled Data
		5.5.1 Lowess and Loess Smoothing
		5.5.2 Splines
		5.5.3 Kernel Density Estimation
	5.6 Filtering Images (2D Filters)
		5.6.1 Representation of Grayscale Images
		5.6.2 Color Images
		5.6.3 Image Transparency
		5.6.4 2D-Filtering
		5.6.5 Morphological Filters for 2D-Data
	5.7 Exercises
	References
6 Event- and Feature-Finding
	6.1 Finding Simple Features
		6.1.1 Example 1: Find Large Signal Values in 1D-Data
		6.1.2 Example 2: Find Start and End of a Movement
		6.1.3 Example 3: Find Bright Pixels in Grayscale Image
	6.2 Cross-Correlation
		6.2.1 Comparing Signals
		6.2.2 Auto-correlation
		6.2.3 Normalization
		6.2.4 Mathematical Implementation
		6.2.5 Features of Cross-Correlation Functions
		6.2.6 Cross-Correlation and Convolution
		6.2.7 Example
	6.3 Interpolation
		6.3.1 Linear Interpolation
		6.3.2 Cubic Spline Interpolation
	6.4 Exercises
	References
7 Statistics
	7.1 Statistical Basics
		7.1.1 Principles of Inferential Statistics
		7.1.2 Common Statistical Parameters
		7.1.3 Normal Distribution
	7.2 Confidence Intervals
		7.2.1 For Data
		7.2.2 Standard Error of the Mean
	7.3 Comparison Tests for Normally Distributed Data
		7.3.1 Comparing Data to a Fixed Value
		7.3.2 Hypothesis Tests
		7.3.3 One-sided versus Two-sided Comparisons
		7.3.4 Comparing Two Independent Groups
		7.3.5 Pre-Post Comparisons
	7.4 Exercises
	References
8 Parameter Fitting
	8.1 Correlations
		8.1.1 Correlation Coefficient
		8.1.2 Coefficient of Determination
	8.2 Straight Lines
		8.2.1 Normal Form of Line Equation
	8.3 Line Fitting
		8.3.1 Residuals
		8.3.2 Least Squares Estimators
	8.4 Linear Fits with Python
		8.4.1 Linear Model without Intercept
		8.4.2 Linear Model with Intercept
		8.4.3 Line-Fit
		8.4.4 Polynomial-Fit
		8.4.5 Sine-Fit
		8.4.6 Circle-Fit
	8.5 Confidence Intervals
		8.5.1 Finding Confidence Intervals
		8.5.2 Confidence Intervals and Hypothesis Tests
		8.5.3 Significance
	8.6 Fitting Nonlinear Functions
	8.7 Exercises
9 Spectral Signal Analysis
	9.1 Transforming Data
	9.2 Fourier Integral
		9.2.1 Definition and Interpretation
		9.2.2 Complex Exponential Notation
		9.2.3 Examples
	9.3 Fourier Series
		9.3.1 Definition
		9.3.2 Applications
	9.4 Discrete/Fast Fourier Transform
	9.5 Spectral Density Estimation
		9.5.1 Periodogram
		9.5.2 Welch Periodogram
	9.6 Fourier Transformation, Convolution, and Cross-Correlation
		9.6.1 Convolution
		9.6.2 Cross-Correlation
	9.7 Time Dependent Fourier Transform
		9.7.1 Windowing
		9.7.2 Example: Human Vowels
	9.8 Exercises
	References
10 Solving Equations of Motion
	10.1 Transfer Functions
		10.1.1 Responses to Sinusoidal Inputs
		10.1.2 Superposition
	10.2 Laplace Transformation
		10.2.1 Parallel Systems
		10.2.2 Serial Systems
		10.2.3 Feedback Systems
	10.3 Implementation of Simulations
		10.3.1 Simulation of Transfer Functions
		10.3.2 Simulation of Feedback
	10.4 Bode Diagram
	10.5 Discrete Versus Continuous Systems
		10.5.1 Laplace Transform Versus Fourier Transform
		10.5.2 Z-Transformation
		10.5.3 Transfer Function and Impulse Response
	10.6 Exercises
	References
11 Machine Learning
	11.1 Example 1: Predicting a Class
	11.2 Example 2: Predicting a Value
	References
12 Useful Programming Tools
	12.1 Debugger
	12.2 Code Versioning with git
		12.2.1 Overview
		12.2.2 Installation and Interfaces
		12.2.3 Examples
	12.3 Test Tools
	12.4 Graphical User Interfaces (GUIs)
		12.4.1 PySimpleGUI—Examples
		12.4.2 PyQtGraph
		12.4.3 Tips for User Interface
	12.5 Exercises
A Python Programs
B Solutions
	B.1  Solutions to Introduction
	B.2  Solutions to Python
	B.3  Solutions to Data Input
	B.4  Solutions to Data Display
	B.5  Solutions to Data Filtering
	B.6  Solutions to Event- and Feature-Finding
	B.7  Solutions to Statistics
	B.8  Solutions to Parameter Fitting
	B.9  Solutions to Spectral Signal Analysis
	B.10  Solutions to Solving Equations of Motion
	B.11  Solutions to Useful Programming Tools
C Abbreviations
D Web Ressources