Most of the real-life signals are non-stationary in nature. The examples of such signals include biomedical signals, communication signals, speech, earthquake signals, vibration signals, etc. Time-frequency analysis plays an important role for extracting the meaningful information from these signals. The book presents time-frequency analysis methods together with their various applications.
The basic concepts of signals and different ways of representing signals have been provided. The various time-frequency analysis techniques namely, short-time Fourier transform, wavelet transform, quadratic time-frequency transforms, advanced wavelet transforms, and adaptive time-frequency transforms have been explained. The fundamentals related to these methods are included. The various examples have been included in the book to explain the presented concepts effectively. The recently developed time-frequency analysis techniques such as, Fourier-Bessel series expansion-based methods, synchrosqueezed wavelet transform, tunable-Q wavelet transform, iterative eigenvalue decomposition of Hankel matrix, variational mode decomposition, Fourier decomposition method, etc. have been explained in the book. The numerous applications of time-frequency analysis techniques in various research areas have been demonstrated.
This book covers basic concepts of signals, time-frequency analysis, and various conventional and advanced time-frequency analysis methods along with their applications. The set of problems included in the book will be helpful to gain an expertise in time-frequency analysis. The material presented in this book will be useful for students, academicians, and researchers to understand the fundamentals and applications related to time-frequency analysis.
Author(s): Ram Bilas Pachori
Publisher: CRC Press
Year: 2023
Language: English
Pages: 237
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Foreword
Preface
Acknowledgments
Author Biography
Chapter 1: Basics of Signals
1.1. Definition of Signal
1.2. Types of Signals
1.2.1. Continuous-Time, Discrete-Time, and Digital Signals
1.2.2. Aperiodic and Periodic Signals
1.2.3. Odd and Even Signals
1.2.4. Causal, Non-Causal, and Anti-Casual Signals
1.2.5. Deterministic and Stochastic Signals
1.2.6. Stationary and Non-Stationary Signals
1.2.7. Single-Channel and Multi-Channel Signals
1.2.8. Energy and Power Signals
1.3. Various Measures of the Signals
1.3.1. Normed Space
1.3.2. Inner Product Space
1.3.2.1. Orthogonality Condition
1.3.3. Metric Space
1.4. Important Signals
1.4.1. Sinusoidal Signals
1.4.2. Unit-Step Function
1.4.3. Impulse Function
1.4.4. Ramp Function
1.5. Signal Operations
1.5.1. Time Shifting
1.5.2. Time Scaling
1.5.3. Time Reversal
1.5.4. Combination of Time Scaling and Shifting
Chapter 2: Signal Representation
2.1. Signal Representation in Terms of Orthogonal Functions
2.2. Signal Representation in Terms of Impulse Functions
2.3. Signal Representation in Terms of General Basis Functions
2.4. Signal Representation in Terms of Complex Exponential Functions
2.4.1. Fourier Series Representation
2.4.2. Fourier Transform
2.5. Signal Representation in Terms of Bessel Functions
2.5.1. Fourier-Bessel Series Expansion
2.5.2. Fourier-Bessel Transform
Chapter 3: Basics of Time-Frequency Analysis
3.1. Time-Domain Representation
3.1.1. The Non-Parametric AFM Signal Model
3.1.2. The Complex Amplitude Modulated Signal Model
3.1.3. The Complex Frequency Modulated Signal Model
3.1.4. The Parametric AFM Signal Model
3.2. Time-Domain Localization
3.3. Frequency-Domain Localization
3.4. Heisenberg Box Representation
3.5. AM and FM Bandwidths
3.6. Spectrum AM and PM Durations
3.7. Uncertainty Principle
3.8. Instantaneous Frequency
3.9. Basic Ideas Related to TFDs
Chapter 4: Short-Time Fourier Transform
4.1. STFT
4.1.1. Narrowband and Wideband Spectrograms
4.2. Time-Frequency Resolution of STFT
4.3. STFT Interpretations
4.3.1. Fourier Spectrum of the Windowed Signal
4.3.2. STFT as Inner Product
4.3.3. STFT as Convolution
4.3.4. Image and Contour Forms
4.4. Reconstruction Process for STFT
4.5. Energy Conservation for STFT
4.6. Short-Frequency Fourier Transform
4.7. Discrete Version of STFT
4.8. Examples of STFT
4.8.1. Time Shifted Signal
4.8.2. Frequency Shifted Signal
4.8.3. Time and Frequency Shifted Signal
Chapter 5: Wavelet Transform
5.1. Continuous Wavelet Transform
5.2. Scalogram
5.3. Features of CWT
5.3.1. Time-Frequency Localization
5.3.2. Constant-Q Analysis
5.3.3. Convolution Form
5.3.4. Singularity Detection
5.4. Inverse CWT
5.5. Some Properties of CWT
5.6. Energy Conservation in CWT
5.7. Wavelet Series
5.7.1. Concept of Frames
5.7.2. Dyadic Sampling
5.7.3. Wavelet Series as Filter Bank
5.8. Discrete Wavelet Transform
5.8.1. Multiresolution Analysis
5.8.2. Two-Scale Relation for Scaling and Wavelet Functions
5.8.3. Conditions on h(n) and g(n)
5.9. DWT Based on Filter Bank
Chapter 6: Quadratic Time-Frequency Transforms
6.1. Quadratic Time-Frequency Transforms
6.1.1. Wigner-Ville Distribution
6.1.1.1. WVD of an Impulse Function
6.1.1.2. WVD of a Complex Exponential Signal
6.1.1.3. WVD of a Chirp Signal
6.1.2. Properties of WVD
6.2. Cross-Term Suppression in WVD
6.2.1. FBSE-Based Technique to Suppress Cross-Term
6.2.2. Pseudo WVD
6.2.3. Smoothed Pseudo WVD
6.2.4. Ambiguity Function
6.2.5. Relationship Between Ambiguity Function and WVD
6.3. General Time-Frequency Distributions
6.3.1. Shift-Invariant Time-Frequency Distributions
6.3.1.1. Wigner-Ville Distribution
6.3.1.2. Choi-Williams Distribution
6.3.1.3. Spectrogram
6.3.2. Affine-Invariant TFDs
6.4. Implementation of Cohen's Class TFDs
Chapter 7: Advanced Wavelet Transforms
7.1. Wavelet Packet Transform
7.2. Synchrosqueezed Wavelet Transform
7.3. Rational-Dilation Wavelet Transforms
7.4. Tunable-Q Wavelet Transform
7.5. Flexible Analytic Wavelet Transform
7.6. FBSE-Based Flexible Analytic Wavelet Transform
7.7. Dual-Tree Complex Wavelet Transform
Chapter 8: Adaptive Time-Frequency Transforms
8.1. Hilbert-Huang Transform
8.1.1. Empirical Mode Decomposition
8.2. Ensemble Empirical Mode Decomposition
8.3. Variational Mode Decomposition
8.4. Empirical Wavelet Transform
8.5. FBSE-Based Empirical Wavelet Transform
8.5.1. Normalized Hilbert Transform
8.6. Fourier Decomposition Method
8.6.1. Fourier Intrinsic Band Function
8.6.2. Continuous Fourier Decomposition Method
8.6.3. Discrete Fourier Decomposition Method
8.7. Iterative Eigenvalue Decomposition of Hankel Matrix
8.8. Dynamic Mode Decomposition
Chapter 9: Applications
9.1. Overview
9.2. Automated Detection of Diseases Using Biomedical Signals
9.2.1. Epileptic Seizure Detection from EEG Signals Based on EMD
9.2.2. Detection of Coronary Artery Disease from ECG Signals
9.3. Disease Detection and Diagnosis from Biomedical Images
9.3.1. Glaucoma Diagnosis Using 2D-FBSE-EWT
9.3.2. Diagnosis of Diabetic Retinopathy and Diabetic Macular Edema Using 2D-FBSE-FAWT
9.4. Extraction of Vital Signs from Physiological Signals
9.4.1. Blood Pressure Delineation
9.4.2. Estimation of HR and RR from PPG Signal Using EEMD and PCA
9.5. Brain-Computer Interface
9.6. TFA for Speech Processing
9.6.1. Robust AM-FM Features for Speech Recognition
9.6.2. Pitch Determination Using HHT
9.7. Applications in Communication Engineering
9.7.1. Mode Identification in Wireless Software-Defined Radio
9.7.2. Jammer Mitigation
9.8. Power Quality Assessment
9.9. Machinery Fault Diagnosis
9.10. Chemical Engineering
9.10.1. Prediction of Different Patterns in IVR
9.10.2. Application in UV Spectroscopy
9.11. Financial Applications
9.12. Ocean Engineering
References
Index
