e178-L11.ppt

e178-L11.ppt - Wavelets: a preview Acknowledgements :...

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Unformatted text preview: Wavelets: a preview Acknowledgements : Material compiled from the MATLAB Wavelet Toolbox User Guide and Chapter 7, DIP 3e. READING: Chapter 7: 7.1.1. ECE 178: a wavelet tour 2 Motivation ECE 178: a wavelet tour 2 Motivation ECE 178: a wavelet tour 3 Problem with Fourier Fourier analysi s -- breaks down a signal into constituent sinusoids of different frequencies. a serious drawback In transforming to the frequency domain, time information is lost. When looking at a Fourier transform of a signal, it is impossible to tell when a particular event took place. ECE 178: a wavelet tour 4 Gabors proposal ECE 178: a wavelet tour 5 Fourier Gabor Wavelet Scale-space decomposition ECE 178: a wavelet tour 6 Localization (or the lack of it) ECE 178: a wavelet tour 7 Fourier decomposition = + + ECE 178: a wavelet tour 8 and the Wavelet decomposition Fourier transfor m: Similarly, the continuous wavelet transform (CWT) is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function : The result of the CWT are many wavelet coefficients C, which are a function of scale and position. ECE 178: a wavelet tour 9 Wavelet decomposition contd....
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e178-L11.ppt - Wavelets: a preview Acknowledgements :...

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