Hi all,
I am using Wavelet module for S-Plus to calculate
the wavelet functions. According to eq (2.2) on p14 in Bruce
and Gao's book (Applied Wavelet Analysis with S-Plus)
the following relationship should hold
phi_{jk} (t) = 2 ^(-j/2) phi(2^(-j)*t - k)
However, when I tried the following
> x0_plot(wavelet("d6",mother=F,shift=0,level=0),plot=F,J=2)
> x1_plot(wavelet("d6",mother=F,shift=0,level=-1),plot=F,J=2)
> x2_plot(wavelet("d6",mother=F,shift=0,level=-2),plot=F,J=2)
> x3_plot(wavelet("d6",mother=F,shift=0,level=-3),plot=F,J=2)
> x1$y/x0$y
[1] NA NA 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 NA
NA
> x2$y/x0$y
[1] NA NA 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 NA
NA
> x3$y/x0$y
[1] NA NA 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 NA
NA
In other words, the above experiments seem to indicate that
phi_{jk} (t) = 2 ^(-j) phi(2^(-j)*t - k)
(i.e. 2 ^(-j/2) is actually 2 ^(-j) in the above calculation)
Does anybody know what's going on here?
Cheers,
Shinn-Juh Lin
School of Finance & Economics
University of Technology, Sydney
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