If we want give a description of a function $f$,
we may do this by giving values $f(t)$ of the function,
The fourier expansion of the function leads to an alternative description.
With some historic remarks and somemotivating examples
I will present the wavelet expansion of functions as a compromise
between those two alternatives to represent functions..
If we want give a description of a function $f$,
we may do this by giving values $f(t)$ of the function,
The fourier expansion of the function leads to an alternative description.
With some historic remarks and somemotivating examples
I will present the wavelet expansion of functions as a compromise
between those two alternatives to represent functions..
The Time-Frequence plane will be introduce and these
representations of functions (mentioned above) will be related to it.
I will describe the Continous Wavelet transform and how it can be
use to analys the "time-frequency contents of a function..
Further, I will discuss several different ways to construct
othonormal wavelet bases. This involves studies of box splines,
multiscale analysis, bi-orthogonal bases, and qadratic- mirror filter,
interpollets, and the scaling equation.
The second hour I want to study the wavelets filters
as Lowpass and Highpass filters, how to build up the wavelet
filter tree.
By a gerneralization of the wavelet filter tree we obtain
the wavelet packets which is a librario of basis functions
which can be used to build an orthonormal basis which is
adapted to the data. This involves setting up a cost function
and finding an algorithm which minimize the cost.This has several
applications as effective compression, noise reduction and feature
extraction.
The Time-Frequence plane will be introduce and these
representations of functions (mentioned above) will be related to it.
I will describe the Continous Wavelet transform and how it can be
use to analys the "time-frequency contents of a function..
Further, I will discuss several different ways to construct
othonormal wavelet bases. This involves studies of box splines,
multiscale analysis, bi-orthogonal bases, and qadratic- mirror filter,
interpollets, and the scaling equation.
The second hour I want to study the wavelets filters
as Lowpass and Highpass filters, how to build up the wavelet
filter tree.
By a gerneralization of the wavelet filter tree we obtain
the wavelet packets which is a librario of basis functions
which can be used to build an orthonormal basis which is
adapted to the data. This involves setting up a cost function
and finding an algorithm which minimize the cost.This has several
applications as effective compression, noise reduction and feature
extraction.
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