“Haar Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Haar Function

释义

Haar Function

Define

(1)

and

(2)

where the Functions plotted above are

Then a Function

can be written as a series expansion by

(3)

The Functions

and

are all Orthogonal in

, with

(4)

(5)

These functions can be used to define Wavelets. Let a Function be defined on

intervals,with

a Power of 2. Then an arbitrary function can be considered as an

-Vector

, and theCoefficients in the expansion

can be determined by solving the Matrix equation

(6)

for

, where

is the Matrix of

basis functions. For example,

(7)

The Wavelet Matrix can be computed in

steps, compared to

for theFourier Matrix.

See also Wavelet, Wavelet Transform

References

Haar, A. ``Zur Theorie der orthogonalen Funktionensysteme.'' Math. Ann. 69, 331-371, 1910.

Strang, G. ``Wavelet Transforms Versus Fourier Transforms.'' Bull. Amer. Math. Soc. 28, 288-305, 1993.

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