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Unformatted text preview: Wavelets Wavelets: (signal processing interpretation) A wavelet can be viewed as a bandpass filter with some upper and lower cutoff frequencies. ( t ) : mother wavelet or a wavelet generating function used to generate a set of bandpass filters that cover the frequency domain in which the signal of interest resides (signal processing interpretation). it is used to generate a set of basis vectors for a signal expansion (mathematical interpretation). F T : < o m F.T. t \ EEE 508 1 Wavelets Family of wavelets generated by shifting and scaling ( t ) 9 Scaling controls bandwidth and center frequency : < o m a a t F.T. 1 \ 9 Shifting allows us to view decomposition in terms of a convolution Basis consisting solely of scaled and shifted versions of a mother wavelet. : < o m a a a a \ 9 Mother wavelet and generated wavelets in family are required to satisfy the admissibility condition: In frequency domain: : f d 2 In time-domain: f : : < f (bounded)...
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This document was uploaded on 03/11/2012.
- Fall '09
- Signal Processing