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   -> Volume 7, Issue 5

Question: Negative wavelet coefficients
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Author Message (Richard Kerns)

PostPosted: Wed Apr 22, 1998 10:21 am    
Subject: Question: Negative wavelet coefficients
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#34 Question: Negative wavelet coefficients

14 April, 1998

Dear Waveleteers,

I recently began learning about Wavelets. I decided to start with
the Haar Wavelet. I obtained a copy of the software package
"Wavelab", which I used with Matlab. I first read about the Haar
functions and the Haar series in a book by K. G. Beauchamp called
"Walsh Functions and their applications" published by Academic Press.

I first tried the function f(x)=1 in the interval from 0 to 1.
Using 64 functional values I obtained 8 for the first Haar coefficient
with the other coefficients being 0. This differs from the value I
had expected by a factor of 8. I understand that this factor of 8
arises as the sqrt. of 64, because I used 64 values. I decided that
in working with wavelab I should change the formula by multiplying by
the norm, which is the sqrt. of the number of functional values used.

I tried another example in the interval from 0 to 1 with
f(x)=2 for x less than 1/2 and f(x) =0 for x greater than 1/2. I
calculated that the first 2 Haar coefficients should be 1 and the rest
0 using the formulae in the book by Beauchamp. When I use 64
functional values to define the function, then I expect using the
changed formula described in the paragraph above, the value 8 for each
of the first two coefficients and 0 for the other coefficients. Using
Wavelab I then found the first coefficient to be 8 as expected, but
the second coefficient was -8. I am not able to explain the negative
sign. After all I had obtained my function by taking the sum of the
first two Haar functions. I would be grateful for any help you may be
be able to give me.
Richard Kerns
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