Time-Frequency Domain for Segmentation and Classification of Non-stationary Signals: The Stockwell Transform Applied on Bio-signals and Electric Signa [Hardcover]

This book focuses on signal processing algorithms based on the timefrequency domain. Original methods and algorithms are presented which are able to extract information from non-stationary signals such as heart sounds and power electric signals. The methods proposed focus on the time-frequency domain, and most notably the Stockwell Transform for the feature extraction process and to identify signatures. For the classification method, the Adaline Neural Network is used and compared with other common classifiers. Theory enhancement, original applications and concrete implementation on FPGA for real-time processing are also covered in this book.

Preface ix

Chapter 1. The Need for TimeFrequency Analysis?1

1.1. Introduction?1

1.2. Stationary and non-stationary concepts?2

1.2.1. Stationarity?2

1.2.2. Non-stationarity 4

1.3. Temporal representations?5

1.4. Frequency representations of signals?6

1.4.1. Fourier transform?7

1.4.2. Mean frequency, bandwidth and frequency average 10

1.5. Uncertainty principle?12

1.6. Limitation of time analysis and frequency analysis: the need for timefrequency representation 15

1.6.1. Instantaneous frequency?15

1.7. Conclusion?18

1.8. Bibliography?19

Chapter 2. TimeFrequency Analysis: The S-Transform?21

2.1. Introduction?21

2.2. Synthetic signals 22

2.3. The STFT?22

2.4. The WT 24

2.5. The WignerVille distribution?25

2.5.1. The pseudo-WVD 27

2.5.2. The smoothed PWVD?27

2.6. Cohens class?28

2.7. The S-transform?29