Title: Discrete Wavelet Transform: From Frames to Fast Wavelet Transform
Abstract: Both the short-time Fourier transform and the continuous wavelet transform can be seen as operators that project the signal s(t) from the one-dimensional time domain into the two-dimensional time-frequency plane. In the case of the continuous wavelet transform the scaling a and delay b are assumed to be continuous in value; that is, it is said that the CWT is defined in the (ℝ+)2 plane where the parameters a and b are continuous in value: ( a ∈ℝ+ and b ∈ℝ ). Since no new information can be created by this transform, the same information contained in the signal s(t) with t ∈ ℝ is available with the CWT. The increase in complexity from t 6 ℝ to (a, b) ∈ (ℝ+)2 results only in a redundant representation of the signal. This redundancy can be reduced by discretizing the transform parameters (a, b). Care must be taken so that we can still achieve reconstruction without any loss of information. Thus, the first question we must answer is how do we sample the parameters (a,b)?
Publication Year: 2002
Publication Date: 2002-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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