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Unformatted text preview: as a linear combination of sinusoids , the idea underlying wavelet analysis is to represent the function as a linear combination of wavelets . In Fourier analysis, each sinusoid is associated with a particular frequency ω . In contrast, each wavelet is associated with two independent variables, time and scale t τ , so that a wavelet is essentially nonzero only inside a particular interval, [ , ] t t − + . Within the interval, a wavelet looks like a "small wave" centered at t . By expanding a time series into wavelets, one can learn how it varies on particular scales across time. Haar wavelets Example 2 How a Haar system approximates the functions from Example 1. Example 3 Northern Hemisphere temperature series. Wavelet Variance...
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.
- Spring '09