Applications in Time-Frequency Signal Processing

Antonia Papandreou-Suppappola

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9780849300653
• eBook ISBN: 9781351835909
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Because most real-world signals, including speech, sonar, communication, and biological signals, are non-stationary, traditional signal analysis tools such as Fourier transforms are of limited use because they do not provide easily accessible information about the localization of a given frequency component. A more suitable approach for those studying non-stationary signals is the use of time frequency representations that are functions of both time and frequency.Applications in Time-Frequency Signal Processing investigates the use of various time-frequency representations, such as the Wigner distribution and the spectrogram, in diverse application areas. Other books tend to focus on theoretical development. This book differs by highlighting particular applications of time-frequency representations and demonstrating how to use them. It also provides pseudo-code of the computational algorithms for these representations so that you can apply them to your own specific problems.Written by leaders in the field, this book offers the opportunity to learn from experts. Time-Frequency Representation (TFR) algorithms are simplified, enabling you to understand the complex theories behind TFRs and easily implement them. The numerous examples and figures, review of concepts, and extensive references allow for easy learning and application of the various time-frequency representations.

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Time–Frequency Processing: Tutorial on Principles and Practice

Antonia Papandreou-Suppappola

Arizona State University

CONTENTS

1.1 Introduction

1.2 Time-varying Signals and their Representation

1.3 Quadratic Time–Frequency Representations

1.4 Matched Time–Frequency Processing for Various Applications

1.5 Applications in Time–Frequency Signal Processing

1.6 Concluding Remarks

Acknowledgments

References

Appendix A: Acronyms in Alphabetical Order

Appendix B: Mathematical Notation in Alphabetical Order

1.1 Introduction

The area of signal processing is founded on a rigorous mathematical exposition that is important for a profound understanding of the subject. The application of these mathematical concepts and techniques is necessitated by the continuous developments in many technologically advanced fields that require the processing of signals to extract important information. Signals convey information to represent measured streams of real-world application-dependent data such as remote-sensing satellite waveforms or seismic waves. For a practical application, a signal can be processed in a multitude of ways to extract specific information that cannot easily be obtained in the time domain. The processing of such signals forms the basis of many applications including analysis, synthesis, filtering, characterization or modeling, modulation, detection, estimation, classification, suppression, cancellation, equalization, coding and synchronization. A classical tool to accommodate this processing is the Fourier transform (FT)* that is widely used to extract frequency information from the time domain signal. However, although successful in a wide range of applications, Fourier theory often possesses intrinsic limitations that depend on the signal to be processed.

1.1.1 Demand for time–frequency processing techniques

The purpose of this tutorial is to aid many signal processing practitioners to comprehend, utilize, conjecture and prove useful the theory on extracting information from signals that are nonstationary or time varying (TV). These signals have frequency content and properties that change with time. This class of signals is very common in real-world occurrences and, as such, it is very important to be able to process the signals as accurately as possible. TV signals include the following: the impulse response of a wireless communications channel, radar and sonar acoustic waves, seismic acoustic waves, biomedical signals such as the electrocardiogram (ECG) or neonatal seizures, biological signals such as bat or dolphin echolocation sounds, vocals in speech, notes in music, engine noise, shock waves in fault structures and jamming interference signals.

The FT does provide the overall frequency information present in a signal. However, it is of limited use for the analysis of TV signals because it does not provide easily accessible information about the signal spectral localization over short periods of time. Some suitable processing tools for these signals are transformations that provide information about the time–frequency (TF) content of the signals. The transformations can be one-dimensional (1-D) TV transforms (TVTs) with basis functions having joint TF characteristics. Specifically, the TVTs could match the instantaneous frequency (IF) of a signal and be functions of the rate of change of the IF. A TVT example is the linear matched signal transform (LMST) that enables the analysis of linear frequency-modulated (FM) chirp signals by presenting them as localized peaks in the linear FM (LFM) rate domain [1, 2].

These transformations can also be two-dimensional (2-D) time–frequency representations (TFRs) of actual time and frequency. The concept of processing in the TF domain dates as early as 1932 when Wigner introduced the Wigner distribution (WD) in the context of quantum mechanics as a function of position and momentum [3]. The WD was reinvented by Ville in 1948 in the cont...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• 1 Time-Frequency Processing: Tutorial on Principles and Practice
• 2 Interference Excision via Time-Frequency Distributions
• 3 Positive Time-Frequency Distributions
• 4 Positive Time-Frequency Distributions and Acoustic Echoes
• 5 Time-Frequency Reassignment: From Principles to Algorithms
• 6 Linear Time-Frequency Filters: On-line Algorithms and Applications
• 7 Discrete Reduced Inteference Distributions
• 8 Time-Frequency Analysis of Seismic Reflection Data
• 9 Time-Frequency Methodology for Newborn EEG Seizure Detection
• 10 Quadratic Time-Frequency Features for Speech Recognition
• Index