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$\sigma$%
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$\kappa \sigma$%
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$\kappa \sigma$%
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${\cal F}^{-1}$%
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${\cal F}$%
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$\displaystyle {\cal F}[x+y]$%
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${\cal F}[x]$%
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$25^\circ$%
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\begin{table}
\begin{tex2html_preform}\begin{verbatim} SCINTILLATION = PHOTON NOISE Photon Noise Present
at secZ = 2.36 secZ = 1.10 of 5.sec.int. FAINT
between between is0.005 mag.at limit
U 9.9 & 8.9 7.1 & 7.0 10.5 5.5
B 10.6 & 9.7 7.6 & 7.5 11.2 6.0
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$\epsilon$%
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\begin{tex2html_preform}\begin{verbatim}u SKY on FEB 14 1993 R = moonrise t = twilight sky
X I ^ ^ ^^
10.I
I t R
3.+ | t
I |
I
I
2.+ * tt
I * $
I $* * * **$** *
I t $* **$$**$*$* $$ * * t
1.+ tt * * $ $$*$*$$$**$*$* ** * $ t
I t * * $$$* $*$$**$
I t ****$* * **
I *$ * $$$$ $
0.+ $
I
I
I
-1.+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+---
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 4E-02
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.01 I
I *
I
-1.+
I *
I * * * *
I
I * * $ +++++++++++++
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I ++++++++++++ * * *
I * * $* $
I * * *
I *
1.+
I *
I
I *
I
2.+---+---+---+---+---+---+---+---+---+---+---+---+---+--
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$ (\epsilon_1 - \epsilon_2 )$%
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$ (\epsilon_1 + \epsilon_2 ) (M_1 - M_2) / (M_1 + M_2 )$%
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$C_{\chi}$%
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$\phi(x)$%
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$\displaystyle c_j(k)=<f(x),2^{-j}\phi( 2^{-j}x-k)>$%
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$\phi(x)$%
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$\hat h(\nu)$%
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$\sum_n
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$\psi(x)$%
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$\tilde g$%
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$\displaystyle c_{j}(k)=2\sum_l [c_{j+1}(l)\tilde h(k+2l)+w_{j+1}(l)\tilde g(k+2l)]$%
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$\tilde H$%
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$\tilde G$%
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$\displaystyle \hat g(\nu)$%
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$\displaystyle e^{-2\pi\nu}\hat h^*(\nu+{1\over 2})$%
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$\displaystyle \hat{\tilde h}(\nu)$%
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$\displaystyle \mid \hat h(\nu) \mid^2+ \mid \hat h(\nu+{1\over 2} \mid^2=1$%
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$\displaystyle e^{-2\pi\nu}\hat{\tilde h}^*(\nu+{1\over 2})$%
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$\displaystyle \hat{\tilde g}(\nu)$%
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$\displaystyle \hat h(\nu)\hat{\tilde h}(\nu)+\hat h^*(\nu+{1\over 2})
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$\{c_1(k)\}$%
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$\{c_0(k)\} -
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{\newpage\clearpage
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$\phi(x)$%
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$\psi(x)$%
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{\newpage\clearpage
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$\displaystyle \frac{1}{2}\psi(\frac{x}{2}) = \phi(x) - \frac{1}{2}\phi(\frac{x}{2})$%
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$\displaystyle c_i(k) = \sum_l h(l) c_{i-1} (k+2^{i-1}l)$%
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{\newpage\clearpage
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$\{h(k)\}$%
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$\phi(x)$%
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$\displaystyle \frac{1}{2}\phi(\frac{x}{2}) = \sum_l h(l) \phi(x-l)$%
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{\newpage\clearpage
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$\displaystyle c_0(k) = c_{n_p}(k) \sum_{j=1}^{n_p} w_j(k)$%
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{\newpage\clearpage
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$\phi$%
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\begin{displaymath}\begin{array}{ll}
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{\newpage\clearpage
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$\phi$%
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{\newpage\clearpage
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$\displaystyle \frac{1}{2}\phi(\frac{x}{2}) = \frac{1}{4}\phi(x+1) + \frac{1}{2}\phi(x) + \frac{1}{4}\phi(x-1)$%
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$\displaystyle c_1(k) = \frac{1}{4} c_0(k-1) + \frac{1}{2} c_0(k) + \frac{1}{4} c_0(k+1)$%
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$\displaystyle c_{j+1}(k) = \frac{1}{4} c_j(k-2^j) + \frac{1}{2} c_j(k) + \frac{1}{4}
c_j(k+2^j)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16029}%
$\psi$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16029}%
$\psi$%
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\lthtmlfigureA{figure14537}%
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\lthtmlinlinemathA{tex2html_wrap_indisplay49774}%
$\displaystyle C_{j+1}(k) = -\frac{1}{4} c_j(k-2^j) + \frac{1}{2} c_j(k)
-\frac{1}{4} c_j(k+2^j)$%
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\lthtmlinlinemathA{tex2html_wrap_inline16033}%
$3 \times 3$%
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\lthtmldisplayA{displaymath15862}%
\begin{displaymath}\left(\begin{array}{ccc}
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\lthtmlinlinemathA{tex2html_wrap_inline16037}%
$\{w_j(k,l)\}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16041}%
$\frac{1}{16},\frac{1}{4},\frac{3}{8},\frac{1}{4},\frac{1}{16}$%
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\lthtmldisplayA{displaymath15863}%
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$\displaystyle c_{j+1}(k) = \sum_l h(l-2k) c_j(l)$%
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\lthtmlfigureA{figure14643}%
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$\displaystyle w_{j+1}(k) = c_j(k) - \tilde{c}_j(k)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16059}%
$\tilde{c}_j$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay49800}%
$\displaystyle \tilde{c}_j(k) = 2 \sum_l h(k-2l) c_j(k)$%
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\lthtmlfigureA{figure14659}%
\begin{figure}
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\lthtmlinlinemathA{tex2html_wrap_indisplay49806}%
$\displaystyle c_{j+1}(n,m) = \sum_{k,l} h(k-2n,l-2m) c_j(k,l)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16065}%
$\tilde{c}_j$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49809}%
$\displaystyle \tilde{c}_j(n,m) = 2 \sum_{k,l} h(n-2l,m-2l) c_{j+1}(k,l)$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16067}%
$N\times N$%
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\lthtmlinlinemathA{tex2html_wrap_inline16069}%
$\frac{4}{3}N^2$%
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\lthtmlfigureA{figure14677}%
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\lthtmlinlinemathA{tex2html_wrap_indisplay49813}%
$\displaystyle w_{j+1}(k) = c_j(k) - \tilde c_j (k)$%
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\lthtmlinlinemathA{tex2html_wrap_inline16071}%
$\tilde c_j$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49816}%
$\displaystyle \tilde{c}_j(k) = \sum_l h(k-l) c_j(k)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49819}%
$\displaystyle c_{j+1}(k) = \sum_l h(l-2k) c_j(l)$%
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\lthtmlinlinemathA{tex2html_wrap_inline14698}%
$\mbox{$\bullet$}$%
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\lthtmlinlinemathA{tex2html_wrap_inline16087}%
$c_0(k)=<f(x),\phi(x-k)>$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16089}%
$\phi(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16091}%
$\nu_c\le {1\over 2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49833}%
$\displaystyle c_1(k)=<f(x),\frac{1}{2}\phi(\frac{x}{2}-k)>$%
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\lthtmlinlinemathA{tex2html_wrap_inline16099}%
$\hat h(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49838}%
$\displaystyle \hat h(\nu)= \left\{
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\right.$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49840}%
$\displaystyle \forall \nu, \forall n \mbox{ }$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49841}%
$\textstyle \hat h(\nu + n) = \hat h(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49844}%
$\displaystyle \hat{c}_{j+1}(\nu)=\hat{c}_{j}(\nu)\hat{h}(2^{j}\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49848}%
$\displaystyle w_{j+1}(k)=<f(x),2^{-(j+1)}\psi(2^{-(j+1)}x-k)>$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49851}%
$\displaystyle \hat{w}_{j+1}(\nu)=\hat{c}_{j}(\nu)\hat g(2^{j}\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49854}%
$\displaystyle \hat g(\nu)= \left\{
\begin{array}{ll}
{\hat{\psi}(2\nu)\over \hat{\phi}(\nu)} & \mbox{if } \mid \nu \mid < \nu_c \\
1 & \mbox{if } \nu_c \leq \mid \nu \mid < {1\over 2}
\end{array}
\right.$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49856}%
$\displaystyle \forall \nu, \forall n \mbox{ }$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49857}%
$\textstyle \hat g(\nu + n) = \hat g(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16113}%
$N+{N\over 2}+\ldots+1=2N$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16115}%
${4\over 3}N^2$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49862}%
$\displaystyle \hat B_l(\nu)={\sin\pi\nu\over\pi\nu}^{l+1}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16123}%
$\phi(\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49869}%
$\displaystyle \hat{\phi}(\nu)={3\over 2}B_3(4\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49871}%
$\displaystyle \phi(x)={3\over 8}[{\sin{\pi x\over 4}\over {\pi x\over
4}}]^4$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16131}%
$\hat \phi(u,v) = {3\over 2}B_3(4r)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16133}%
$r = \sqrt(u^2+v^2)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16137}%
$\psi$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16151}%
$\hat g(2^ju,2^jv)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16159}%
$\hat h(2^ju,2^jv)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16169}%
$j \leq n_p$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16171}%
$\{w_1, w_2, \dots, w_{n_p}, c_{n_p}\}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49904}%
$\displaystyle \hat \psi(2\nu) = \hat \phi(\nu) - \hat \phi(2\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49906}%
$\displaystyle \hat g(\nu) = 1 - \hat h(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16173}%
$\hat w_j(\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16175}%
$\hat c_{j-1}(\nu) - \hat c_j(\nu)$%
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\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16177}%
${\cal W} = \{w_1, w_2, \dots, w_{n_p}, c_{n_p}\}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49911}%
$\displaystyle \hat c_0(\nu) = \hat c_{n_p}(\nu) + \sum_j \hat w_j(\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49913}%
$\displaystyle \hat c_{j+1} = \hat h(2^j \nu) \hat c_j(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49914}%
$\displaystyle \hat w_{j+1} = \hat g(2^j \nu) \hat c_j(\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16189}%
$\hat c_j(\nu)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49922}%
$\displaystyle \hat p_h(2^j\nu)|\hat c_{j+1}(\nu)-\hat h(2^j\nu)\hat c_j(\nu)|^2 +
\hat p_g(2^j\nu)|\hat w_{j+1}(\nu)-\hat g(2^j\nu)\hat
c_j(\nu)|^2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16191}%
$\hat p_h(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16193}%
$\hat p_g(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16195}%
$\hat c_j(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16197}%
$\hat c_j(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49928}%
$\displaystyle \hat{c}_{j}(\nu)=\hat{c}_{j+1}(\nu) \hat{\tilde h}(2^{j}\nu)
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\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49930}%
$\displaystyle \hat{\tilde h}(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49931}%
$\textstyle = {\hat{p}_h(\nu) \hat{h}^*(\nu)\over \hat{p}_h(\nu)
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{\newpage\clearpage
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$\displaystyle \hat{\tilde g}(\nu)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49933}%
$\textstyle = {\hat{p}_g(\nu) \hat{g}^*(\nu)\over \hat p_h(\nu)
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49936}%
$\displaystyle \mid \hat \psi(2\nu)\mid^2 = \mid \hat \phi(\nu)\mid^2 - \mid \hat
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16199}%
$\hat{\phi}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16201}%
$\hat{\psi}$%
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{\newpage\clearpage
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{\newpage\clearpage
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$\hat{\tilde{h}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16205}%
$\hat{\tilde{g}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16203}%
$\hat{\tilde{h}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16205}%
$\hat{\tilde{g}}$%
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{\newpage\clearpage
\lthtmlfigureA{figurestar14850}%
\begin{figure*}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16211}%
$\hat{w}_j$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16213}%
$\hat{\tilde{g}}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16215}%
$\hat{c}_j$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16217}%
$\hat{\tilde{h}}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16219}%
$\hat{w}_j\hat{\tilde{g}}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16221}%
$\hat{c}_i\hat{\tilde{h}}$%
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\stepcounter{section}
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\begin{figure}
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$\mbox{$\bullet$}$%
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$\mbox{$\bullet$}$%
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$\displaystyle h(x)=\int_{-\infty}^{+\infty} f(u)g(x-u)dx$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16227}%
$\psi(x)$%
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\lthtmlinlinemathA{tex2html_wrap_inline16229}%
$\chi(x)$%
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\lthtmlinlinemathA{tex2html_wrap_indisplay49968}%
$\displaystyle C=\int_0^{+\infty} \frac{\hat{\psi}^*(\nu)\hat{\chi}(\nu)}{\nu}d\nu$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16235}%
$\psi(x)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49973}%
$\displaystyle W_g(a,b)=\frac{1}{\sqrt a}\int_{-\infty}^{+\infty}g(x)\psi^*(\frac{x-b}{a})dx$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16239}%
$\chi(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49977}%
$\displaystyle g(x)=\frac{1}{C}\int_0^{+\infty}\int_{-\infty}^{+\infty}\frac{1}{\sqrt a}
W_g(a,b)\chi(\frac{x-b}{a})\frac{dadb}{a^2}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49979}%
$\displaystyle h(x)=\frac{1}{C}\int_0^{+\infty}\frac{da}{a^{\frac{5}{
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W_g(a,b)db\int_{-\infty}^{+\infty}f(u)\chi(\frac{x-u-b}{a}) du$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16241}%
$\tilde{\chi}(x)=\chi(-x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16247}%
$\tilde{\chi}(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49985}%
$\displaystyle \tilde W_f(a,b)=\frac{1}{\sqrt
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49987}%
$\displaystyle h(x)=\frac{1}{C}\int_0^{+\infty}\frac{da}{a^2}\int_{-\infty}^{+\infty}
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay49989}%
$\displaystyle h(x)={1\over C}\int_0^{+\infty}\tilde W_f(a,x)\otimes W_g(a,x)\frac{da}{
a^2}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16249}%
$\tilde W_f(a,b)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16253}%
$\tilde{\chi}(x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16259}%
$\psi (x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline15023}%
$\mbox{$\bullet$}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16269}%
$N\log_2N$%
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\stepcounter{subsection}
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\lthtmlinlinemathA{tex2html_wrap_indisplay50007}%
$\displaystyle P(w_i/W_i) = \frac{1}{\sqrt{2\pi}B_i} e^{- \frac{(w_i-W_i)^2} {2B_i^2}}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50011}%
$\displaystyle P(W_i) = \frac{1}{\sqrt{2\pi}S_i}e^{-\frac{W_i^2}{2S_i^2}}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50013}%
$\displaystyle \int_{-\infty}^{+\infty} \psi^*(x) dx = 0$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50017}%
$\displaystyle P(W_i/w_i) = \frac{P(W_i)P(w_i/W_i)}{P(w_i)}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50019}%
$\displaystyle P(W_i/w_i) = \frac{1}{\sqrt{2\pi}\beta_i}e^{-\frac{(W_i-\alpha_i
w_i)^2}{2\beta_i^2}}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50021}%
$\displaystyle \alpha_i = \frac{S_i^2}{S_i^2+B_i^2}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50024}%
$\displaystyle m = \alpha_i w_i$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50026}%
$\displaystyle \beta_i^2 = \frac{S_i^2B_i^2}{S_i^2 + B_i^2}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16291}%
$\alpha_i w_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16293}%
$\alpha_i$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16305}%
$3\sigma$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16317}%
$\alpha_i = \frac{S_i^2}{S_i^2+B_i^2}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16319}%
$W_i = \alpha_i w_i$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50059}%
$\displaystyle P(W_i/w_h) = \frac{1}{\sqrt{2\pi}T_i}e^{-\frac{(W_i- w_h)^2}{2T_i^2}}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50064}%
$\displaystyle P(W_i/w_i \mbox{ and } w_h) = \frac{1}{\sqrt{2\pi}\beta_i}
e^{-\frac{(W_i-\alpha_i w_i)^2}{2\beta_i^2}} \frac{1}{\sqrt{2\pi}T_i}
e^{-\frac{(W_i-w_h)^2}{2T_i^2}}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50066}%
$\displaystyle \beta_i^2 = \frac{S_i^2B_i^2}{S^2 + B_i^2}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50068}%
$\displaystyle \alpha_i = \frac{S_i^2}{S_i^2+B_i^2}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50070}%
$\displaystyle W_i = \frac{T_i^2}{B_i^2+T_i^2+Q_i^2} w_i +
\frac{B_i^2}{B_i^2+T_i^2+Q_i^2} w_h$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50072}%
$\displaystyle Q_i^2 = \frac{T_i^2B_i^2}{S_i^2}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16353}%
$S_i \ll B_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16357}%
$W_i \rightarrow 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16359}%
$B_i \ll S_i \ll T$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16361}%
$W_i \rightarrow w_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16363}%
$B_i \ll T_i \ll S$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16365}%
$W_i \rightarrow w_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16367}%
$T_i \ll B_i \ll S$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16369}%
$W_i \rightarrow w_h$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline15108}%
$\mbox{$\bullet$}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16401}%
$W_i = \frac{T_i^2}{B_i^2+T_i^2+Q_i^2} w_i + \frac{B_i^2}{B_i^2+T_i^2+Q_i^2} w_h$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50121}%
$\displaystyle \mbox{ if } \mid w_i \mid < k B_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50122}%
$\displaystyle \mbox{ if } \mid w_i \mid \geq k B_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16423}%
$W_i^{(s)}(x) \neq 0$%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{eqnarraystar15146}%
\begin{eqnarray*}W_i(x) = & w_i(x) & \mbox{ if } \mid w_i(x) \mid \geq L \\
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\end{eqnarray*}%
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{\newpage\clearpage
\lthtmldisplayA{eqnarraystar15150}%
\begin{eqnarray*}\mbox{ if } \mid w_i(x) \mid \geq kB_i & \mbox{ then } L = & kB_i \\
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\end{eqnarray*}%
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{\newpage\clearpage
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$a \geq k$%
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{\newpage\clearpage
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$t(a) = 1 - \frac{1}{k} a$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline15158}%
$\mbox{$\bullet$}$%
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{\newpage\clearpage
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$\tilde{I}(i,j)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50161}%
$\displaystyle C_{or} = \frac{ \sum_{i = 1}^{N}\sum_{j = 1}^{N} I(i,j)
\tilde{I}(i,j)} {\sqrt{ \sum_{i = 1}^{N}\sum_{j =
1}^{N} I^2(i,j) \sum_{i = 1}^{N}\sum_{j = 1}^{N}
\tilde{I}^2(i,j)}}$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50163}%
$\displaystyle E_{ms}^2 = \frac{1}{N^2} \sum_{i = 1}^{N}\sum_{j = 1}^{N}(I(i,j)-
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50166}%
$\displaystyle E_{nms}^2 = \frac{\sum_{i = 1}^{N}\sum_{j = 1}^{N}(I(i,j)- \tilde{I}(i,j))^2}
{\sum_{i = 1}^{N}\sum_{j = 1}^{N}I^2(i,j)}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50168}%
$\displaystyle SNR_{dB} = 10 \log_{10} \frac{1}{E_{nms}^2} \mbox{ dB}$%
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{\newpage\clearpage
\lthtmlfigureA{figure15217}%
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$\displaystyle \hat I(u,v)= \hat O(u,v) \hat P(u,v) + \hat N(u,v)$%
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{\newpage\clearpage
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$\parallel I(x,y) - P(x,y) * O(x,y) \parallel^2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50181}%
$\displaystyle O^{(n+1)} (x,y) = O^{(n)} (x,y) + \alpha(I(x,y) - P(x,y)* O^{(n)} (x,y))$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16481}%
$\alpha$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16485}%
$\parallel I(x,y) - P(x,y)* O(x,y)
\parallel^2$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50186}%
$\displaystyle O^{(n+1)} (x,y) = O^{(n)} (x,y) + \alpha P_s(x,y) * [I(x,y) - P(x,y) *
O^{(n)} (x,y)]$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50189}%
$\displaystyle \parallel I(x,y) - P(x,y)* O(x,y) \parallel^2 + \lambda \parallel H *
O\parallel^2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16491}%
$\parallel I(x,y) - P(x,y)* O(x,y) \parallel^2$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16495}%
$\lambda \parallel H * O\parallel^2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16497}%
$\lambda$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16499}%
$\lambda$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50197}%
$\displaystyle O^{(n+1)} = O^{(n)} [ \frac{I}{I^{(n)}} \ast P^* ]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50199}%
$\displaystyle I^{(n)} = P \ast O^{(n)}$%
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\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50204}%
$\displaystyle \hat{w}_j^{(I)}(u,v)$%
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\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50205}%
$\displaystyle \hat{g}(2^{j-1}u, 2^{j-1}v)
\prod_{i=j-2}^{i=0}\hat{h}(2^{i}u, 2^{i}v) \hat{I}(u,v)$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50206}%
$\displaystyle {\hat{\psi}(2^{j}u, 2^{j}v) \over
\hat{\phi}(u,v)} \hat{P}(u,v) \hat{O}(u,v)$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50207}%
$\displaystyle \hat{w}_j^{(P)} \hat{O}(u,v)$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay50213}%
$\displaystyle \parallel {\hat \psi(2^ju, 2^jv)\over \hat\phi(u, v)} \hat P(u,v) \hat O(u,v) - \hat w_j^{(I)}(u,v)\parallel^2$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}
{\newpage\clearpage
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$\displaystyle \parallel {\hat \phi(2^{n-1}u, 2^{n-1}v)\over \hat\phi(u, v)} \hat P(u,v) \hat O(u,v) - \hat c_{n-1}^{(I)}(u,v)\parallel^2$%
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