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\samepage \parbox{5in} {Two-channel filter bank:  Separate the input into frequency bands (filter and downsample).  Then reassemble (upsample and filter).}
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\samepage \begin{tabular}{ll}
{\bf  PR Condition} & {\it Perfect reconstruction}. \\  
&The synthesis bank inverts
the analysis bank, with $\ell$ delays.  \\ 
&Biorthogonal banks with no aliasing and no distortion. \\  \\ 
{\bf  Condition O} &{\it Orthogonality}.  \\ 
& The analysis bank is inverted by its transpose.  \\ 
& The wavelets are orthogonal to all their dilates and translates.\\  \\ 
{\bf  Condition $A_{p}$}& {\it Accuracy of order $p$ for
approximation by scaling functions} $\phi(t-k)$.\\ 
&$p$ vanishing moments in the wavelets.  \\ 
&$p$th order decay of wavelet coefficients for smooth $f(t)$.\\  \\ 
{\bf  Condition E} &{\it Eigenvalue condition on the cascade algorithm}.\\ 
&Determines convergence to $\phi(t)$ and smoothness of wavelets.\\ 
&Equivalent to stability of the wavelet basis.\\  \\ 
\end{tabular}
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