By Napler Addison
Contents
Preface bankruptcy 1: Getting all started bankruptcy 2: the continual wavelet remodel 2.1 advent 2.2 The Wavelet 2.3 specifications for the Wavelet 2.4 The power Spectrum of the Wavelet 2.5 The Wavelet remodel 2.6 identity of Coherent buildings 2.7 part Detection 2.8 The Inverse Wavelet remodel 2.9 The sign power: Wavelet established power and tool Spectra 2.10 The Wavelet remodel by way of the Fourier remodel 2.11 complicated Wavelets: The Morlet Wavelet 2.12 The Wavelet rework, few minutes Fourier remodel and Heisenberg containers 2.13 Adaptive Transforms: Matching objectives 2.14 Wavelets in or extra Dimensions 2.15 The CWT: Computation, Boundary results and Viewing 2.16 Endnotes 2.16.1 bankruptcy key terms and words 2.16.2 additional assets bankruptcy three: The Discrete Wavelet remodel 3.1 creation 3.2 Frames and Orthogonal Wavelet Bases 3.2.1 Frames 3.2.2 Dyadic Grid Scaling and Orthonormal Wavelet Transforms 3.2.3 The Scaling functionality and the Multiresolution illustration 3.2.4 The Scaling Equation, Scaling Coefficients and linked Wavelet Equation 3.2.5 The Haar Wavelet 3.2.6 Coefficients from Coefficients: the quick Wavelet remodel 3.3 Discrete enter indications of Finite size 3.3.1 Approximations and information 3.3.2 The Multiresolution set of rules - An instance 3.3.3 Wavelet strength 3.3.4 replacement Indexing of Dyadic Grid Coefficients 3.3.5 an easy labored instance: The Haar Wavelet remodel 3.4 every thing Discrete 3.4.1 Discrete Experimental enter indications 3.4.2 Smoothing, Thresholding and Denoising 3.5 Daubechies Wavelets 3.5.1 Filtering 3.5.2 Symmlets and Coiflets 3.6 Translation Invariance 3.7 Biorthogonal Wavelets 3.8 Two-Dimensional Wavelet Transforms 3.9 Adaptive Transforms: Wavelet Packets 3.10 Endnotes 3.10.1 bankruptcy keyword phrases and words 3.10.2 additional assets bankruptcy four: FLUIDS 4.1 advent 4.2 Statistical Measures 4.2.1 Moments, strength and gear Spectra 4.2.2 Intermittency and Correlation 4.2.3 Wavelet Thresholding 4.2.4 Wavelet choice utilizing Entropy Measures 4.3 Engineering Flows 4.3.1 Jets, Wakes, Turbulence and Coherent constructions 4.3.2 Fluid-Structure interplay 4.3.3 Two-Dimensional stream Fields 4.4 Geophysical Flows 4.4.1 Atmospheric strategies 4.4.2 Ocean procedures 4.5 different purposes in Fluids and extra assets bankruptcy five: ENGINEERING checking out, tracking AND CHARACTERISATION 5.1 creation 5.2 Machining tactics: keep watch over, Chatter, put on and Breakage 5.3 Rotating equipment 5.3.1 Gears 5.3.2 Shafts, Bearings and Blades 5.4 Dynamics 5.5 Chaos 5.6 Non-Destructive trying out 5.7 floor Characterisation 5.8 different functions in Engineering and extra assets 5.8.1 Impacting 5.8.2 info Compression 5.8.3 Engines 5.8.4 Miscellaneous bankruptcy 6: medication 6.1 advent 6.2 The Electrocardiogram 6.2.1 ECG Timing, Distortions and Noise 6.2.2 Detection of Abnormalities 6.2.3 center cost Variability 6.2.4 Cardiac Arrhythmias 6.2.5 ECG information Compression 6.3 Neuroelectric Waveforms 6.3.1 Evoked Potentials and Event-Related Potentials 6.3.2 Epileptic Seizures and Epileptogenic Foci 6.3.3 class of the EEG utilizing synthetic Neural Networks 6.4 Pathological Sounds, Ultrasounds and Vibrations 6.4.1 Blood move Sounds 6.4.2 center Sounds and middle premiums 6.4.3 Lung Sounds 6.4.4 Acoustic reaction 6.5 Blood move and Blood strain 6.6 clinical Imaging 6.6.1 Ultrasonic photos 6.6.2 Magnetic Resonance Imaging, Computed Tomography and different Radiographic photos 6.6.3 Optical Imaging 6.7 different functions in medication 6.7.1 Electromyographic indications 6.7.2 Sleep Apnea 6.7.3 DNA 6.7.4 Miscellaneous 6.7.5 additional assets bankruptcy 7: FRACTALS, FINANCE, GEOPHYSICS AND different parts 7.1 advent 7.2 Fractals 7.2.1 precisely Self-Similar Fractals 7.2.2 Stochastic Fractals 7.2.3 Multifractals 7.3 Finance 7.4 Geophysics 7.4.1 houses of Subsurface Media 7.4.2 floor Fea
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Extra resources for The Illustrated Wavelet Transform Handbook
Example text
Modulus maxima of a composite signal. (a) A composite signal (bottom right) constructed from the noise, curtailed sinusoid and exponential decay signals shown. (b) Wavelet transform plot of the composite signal (Mexican hat wavelet). (c) Modulus maxima plot corresponding to the transform plol in (b). 21) and the analysis of multi fractal signals in chapter 7. 19) The signal energy: wavelet-based energy and power spectra 29 For this equation to be useful the signal must contain finite energy. e.
909 (right). 909 (right). 25. 909 (arbitrary axis units). 849 (arbitrary axis units). 318 (arbitrary axis units). (Note that the Fourier spikes are shown with a finite height and width as they were calculated numerically using a discrete Fourier algorithm. 23(c). 909. 25. We can see the greater degree of frequency localization as fo increases (and hence the number of cycles within the Gaussian envelope increases). 24. 26 shows two signals containing repeating features-bumps and spikes. The transform plots are plotted below the signals.
C) Heisenberg boxes in the time-frequency plane for the STFT. Other window lengths will produce longer and thinner or shorter and fatter boxes. However, once the window length is fixed, all Heisenberg boxes in the time-frequency plane corresponding to the STFT will have the same dimensions. plane for the mother wavelet, and hence the relative locations for all dilated wavelets. 29(b). Thus, when comparing Heisenberg boxes centred at the same location in the time-frequency plane, lower values of fo correspond to Heisenberg boxes that are wider in frequency and narrower in time than boxes corresponding to higher ios.