wavelet
wavelet A basis function, W, that yields the representation of a function f(x) of the form: f(x) = ∑bjkW(2jx – k)
Wavelets are based on two fundamental ideas: dilation and translation. The construction of wavelets begins with the solution to a dilation equation: φ(x) = ∑ckφ(2x – k)
φ(x) is called the scaling function. W can then be derived from φ(x): W(x) = ∑(–1)kc1–kφ(2x – k)
Wavelets are particularly useful for representing functions that are local in time and frequency. The idea of wavelets grew out of seismic analysis and is now a rapidly developing area in mathematics. There are elegant recursive algorithms for decomposing a signal into its wavelet coefficients and for reconstructing a signal from its wavelet coefficients.
Wavelets are based on two fundamental ideas: dilation and translation. The construction of wavelets begins with the solution to a dilation equation: φ(x) = ∑ckφ(2x – k)
φ(x) is called the scaling function. W can then be derived from φ(x): W(x) = ∑(–1)kc1–kφ(2x – k)
Wavelets are particularly useful for representing functions that are local in time and frequency. The idea of wavelets grew out of seismic analysis and is now a rapidly developing area in mathematics. There are elegant recursive algorithms for decomposing a signal into its wavelet coefficients and for reconstructing a signal from its wavelet coefficients.
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