\newcommand{\margin}{\textwidth 6.0 in
	\oddsidemargin 0.2 in
	\evensidemargin  0.2 in
	\textheight 9.0 in
	\topmargin -0.65 in
}
\newcommand{\wmargin}{\textwidth 6.5 in
	\oddsidemargin 0 in
	\evensidemargin 0 in
	\textheight 9.5 in
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\newcommand{\wwmargin}{	\textwidth 7.5 in
	\oddsidemargin -0.5 in
	\evensidemargin  -0.5 in
	\textheight 10.0 in
	\topmargin -1.0 in
} 
\newcommand{\artmargin}{\margin
	\renewcommand{\baselinestretch}{1.8}
   \renewcommand{\arraystretch}{1.3}}

\newcommand{\rutlogo}{\begin{center}
\rule[-2 mm]{5.5 cm}{0.1 cm}\\
\raisebox{1 mm}{\tiny THE STATE UNIVERSITY OF NEW JERSEY}\\
{\Huge\bf RUTGERS}\\
\rule[2 mm]{5.5 cm}{0.1 cm}\\
{\small College of Engineering}\\
{\small Department of Electrical and Computer Engineering}\\[1 cm]  
\end{center}}

	\newtheorem{theorem}{Theorem}
	\newtheorem{thm}{Theorem}
	\newtheorem{conjecture}[theorem]{Conjecture}
	\newtheorem{lemma}{Lemma}
\newcommand{\examp}[1]{\begin{example}#1\end{example}}
\newenvironment{example}{\par\begin{quotation}\small\noindent{\bf Example:\ }}{\end{quotation}\par}
\newenvironment{define}{\par\begin{quotation}\noindent{\bf Definition:\ }}{\end{quotation}\par}

\newenvironment{Proof}[1]{\medskip\par\noindent 
{\bf Proof:\, #1}\,}{{\mbox{\,$\bullet$}\par}}

		  \newcommand{\farrow}[1]{
		  \mbox{
		  \hspace{0 pt}
		  \setlength{\unitlength}{1 pt}	
		  \begin{picture}(#1,10)\thicklines
		  \put(0,5){\vector(1,0){#1}}
		  \end{picture}
		  \hspace{0 pt}
		  }
		  }

		  \newcommand{\barrow}[1]{
		  \mbox{
		  \hspace{0 pt}
		  \setlength{\unitlength}{1 pt}	
		  \begin{picture}(#1,10)\thicklines
		  \put(#1,5){\vector(-1,0){#1}}
		  \end{picture}
		  \hspace{0 pt}
		  }
		  }
		  \newcommand{\midfarrow}[1]{
		  \mbox{
		  \hspace{0 pt}
		  \setlength{\unitlength}{0.1\baselineskip}	
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		  \put(0,5){\vector(1,0){#1}}
		  \end{picture}
		  \hspace{0 pt}
		  }
		  }

		  \newcommand{\midbarrow}[1]{
		  \mbox{
		  \hspace{0 pt}
		  \setlength{\unitlength}{0.1\baselineskip}
		  \begin{picture}(#1,10)\thicklines
		  \put(#1,5){\vector(-1,0){#1}}
		  \end{picture}
		  \hspace{0 pt}
		  }
		  }

	\newcommand{\transpair}[4]{$$#1
		{ { {\displaystyle #2} \atop \farrow{120} } 
		\atop
	     { \barrow{120} \atop {\displaystyle #4} } } #3$$}


% Box Commands
	\newcommand{\skipspace}{\vspace{0.2 in}}

	\newcommand{\posbox}[2]{\begin{minipage}[#1]{\textwidth}
				\begin{tabbing} #2
			\end{tabbing}\end{minipage}}
	\newcommand{\topbox}[1]{\posbox{t}{#1}}
	\newcommand{\botbox}[1]{\posbox{b}{#1}}
	\newcommand{\fitbox}[1]{\posbox{c}{#1}}
\newcommand{\newframe}[1]{\fbox{\shortstack{#1}}}
\newcommand{\topframe}[1]{\begin{tabular}[t]{c}\newframe{#1}\end{tabular}}
\newcommand{\botframe}[1]{\begin{tabular}[b]{c}\newframe{#1}\end{tabular}}

\newcommand{\cframe}[1]{\mbox{\begin{tabular}[c]{|c|}\hline #1 \\ \hline\end{tabular}}}
\newcommand{\icframe}[1]{\mbox{\begin{tabular}[c]{c} #1\end{tabular}}}

% Referencing Commands
	\newcommand{\eqnref}[1]{(\ref{eqn:#1})}
	\newcommand{\Eqnref}[1]{Equation~(\ref{eqn:#1})}
	\newcommand{\eqnlabel}[1]{\label{eqn:#1}}
	\newcommand{\Pref}[1]{page~\pageref{#1}}
	\newcommand{\thmref}[1]{(\ref{thm:#1})}
	\newcommand{\Thmref}[1]{Theorem~\ref{thm:#1}}
	\newcommand{\thmlabel}[1]{\label{thm:#1}}

% Math Commands
	\newcommand{\mod}{\mbox{mod}\ }
	\newcommand{\infsum}[1]{\symsum{#1}{\infty}}
	\newcommand{\symsum}[2]{\sum_{#1=-#2}^{#2}}
	\newcommand{\symint}[1]{\int_{-#1}^{#1}}
	\newcommand{\sumzi}[1]{\sum_{#1=0}^{\infty}}
	\newcommand{\sumoi}[1]{\sum_{#1=1}^{\infty}}
	\newcommand{\infint}{\symint{\infty}}
	\newcommand{\seq}[3]{{#1}_{#2},\ldots,{#1}_{#3}}
	\newcommand{\setseq}[3]{\set{{#1}_{#2},\ldots,{#1}_{#3}}}
	\newcommand{\numseq}[3]{ {#3},{#1}_{#2},\ldots,{#1}_{#3} }
	\newcommand{\prob}[1]{P\braces{#1}}
	\newcommand{\pword}[1]{\prob{\mbox{#1}}}
	\newcommand{\real}[1]{\mbox{Re}\paren{#1}}
	\newcommand{\sgn}{\mbox{sgn}\,}
	\newcommand{\stdev}[1]{\sigma_{#1}}
	\newcommand{\E}[1]{E\bracket{#1}}
	\newcommand{\VAR}[1]{\mbox{VAR}\bracket{#1}}
	\newcommand{\var}[1]{\sigma^2_{#1}}
	\newcommand{\avg}[1]{\overline{#1}}
	\newcommand{\timeavg}[1]{\left\langle #1 \right\rangle}
	\newcommand{\set}[1]{\{#1\}}
	\newcommand{\abs}[1]{\left| #1 \right|}
	\newcommand{\ip}[2]{{\left\langle #1,#2\right\rangle}}
% Greek ans Script Letter Shorthands
\newcommand{\D}{\Delta}
\newcommand{\W}{\Omega}
\newcommand{\Dw}{\Delta\omega}
\newcommand{\F}[1]{{\cal F}\braces{#1}}
\newcommand{\Finverse}[1]{{\cal F}^{-1}\braces{#1}}
\newcommand{\w}{\omega}
	\newcommand{\columnvec}[1]{\bracket{\begin{array}{c} #1 \end{array}}}
	\newcommand{\leftp}{\!\left(}
	\newcommand{\paren}[1]{\left({#1}\right)}
	\newcommand{\parfrac}[2]{\paren{\frac{#1}{#2}}}   
   \newcommand{\bracket}[1]{{\left [{#1}\right ]}}
   \newcommand{\braces}[1]{{\left\{ {#1}\right\}}}
	\newcommand{\eval}[1]{{\left.{#1}\right|}}
	\newcommand{\ceiling}[1]{{\left\lceil #1\right\rceil}}
	\newcommand{\floor}[1]{{\left\lfloor #1 \right\rfloor}}
	\newcommand{\bigfrac}[2]{\frac{\displaystyle #1}{\displaystyle #2}}
   \newcommand{\bigparfrac}[2]{\parfrac{\displaystyle #1}{\displaystyle #2}}
	\newcommand{\onedef}[2]{\begin{array}{ll} 
		\displaystyle {#1}{#2}
		\end{array}}
	\newcommand{\twodef}[4]{\left\{\begin{array}{ll} 
		\displaystyle {#1} & {#2} \\
		\displaystyle {#3} & {#4}
		\end{array}\right.}
	\newcommand{\threedef}[6]{\left\{\begin{array}{ll} 
		\displaystyle {#1} & {#2} \\
		\displaystyle {#3} & {#4}\\
		\displaystyle {#5} & {#6}
		\end{array}\right.}
	\newcommand{\fourdef}[8]{\left\{\begin{array}{ll} 
		\displaystyle {#1} & {#2} \\
		\displaystyle {#3} & {#4}\\
		\displaystyle {#5} & {#6}\\
		\displaystyle {#7} & {#8}
		\end{array}\right.} 
	\newcommand{\Berndist}[2]{\twodef{1}{\mbox{#1}}{0}{\mbox{#2}}}
	\newcommand{\ow}{\mbox{otherwise}}

	\newcommand{\deriv}[3]{\frac{d^{#1}#2}{d{#3}^{#1}}}
	\newcommand{\derivf}[3]{\deriv{#1}{#2(#3)}{#3}}

	\newcommand{\bx}{\mbox{\boldmath $x$}}
	\newcommand{\by}{\mbox{\boldmath $y$}}
	\newcommand{\bu}{\mbox{\boldmath $u$}}
	\newcommand{\bv}{\mbox{\boldmath $v$}}
	\newcommand{\bz}{\mbox{\boldmath $z$}}
	\newcommand{\bX}{\mbox{\boldmath $X$}}
	\newcommand{\bY}{\mbox{\boldmath $Y$}}
	\newcommand{\bU}{\mbox{\boldmath $U$}}
	\newcommand{\bR}{\mbox{\boldmath $R$}}
	\newcommand{\bS}{\mbox{\boldmath $S$}}
	\newcommand{\bC}{\mbox{\boldmath $C$}}
	\newcommand{\boldf}{\mbox{\boldmath $f$}}
	\newcommand{\boldg}{\mbox{\boldmath $g$}}
	\newcommand{\boldF}{\mbox{\boldmath $F$}}
	\newcommand{\boldphi}{\mbox{\boldmath $\phi$}}

	\newcommand{\Ahat}{{\hat{A}}}
	\newcommand{\Bhat}{{\hat{B}}}
        \newcommand{\Chat}{{\hat{C}}}
        \newcommand{\Dhat}{{\hat{D}}}
	\newcommand{\Ehat}{{\hat{E}}}
	\newcommand{\Fhat}{{\hat{F}}}
	\newcommand{\Ghat}{{\hat{G}}}
	\newcommand{\Hhat}{{\hat{H}}}
	\newcommand{\Ihat}{{\hat{I}}}
	\newcommand{\Jhat}{{\hat{J}}}
	\newcommand{\Khat}{{\hat{K}}}
	\newcommand{\Lhat}{{\hat{L}}}
	\newcommand{\Mhat}{{\hat{M}}}
	\newcommand{\Nhat}{{\hat{N}}}
	\newcommand{\Ohat}{{\hat{O}}}
	\newcommand{\Phat}{{\hat{P}}}
	\newcommand{\Qhat}{{\hat{Q}}}
	\newcommand{\Rhat}{{\hat{R}}}
	\newcommand{\Shat}{{\hat{S}}}
	\newcommand{\That}{{\hat{T}}}
	\newcommand{\Uhat}{{\hat{U}}}
        \newcommand{\Vhat}{{\hat{V}}}	
	\newcommand{\What}{{\hat{W}}}
	\newcommand{\Xhat}{{\hat{X}}}
	\newcommand{\Yhat}{{\hat{Y}}}
        \newcommand{\Zhat}{{\hat{Z}}}
   \newcommand{\ahat}{{\hat{a}}}
   \newcommand{\bhat}{{\hat{b}}}
   \newcommand{\chat}{{\hat{c}}}
   \newcommand{\dhat}{{\hat{d}}}
   \newcommand{\ehat}{{\hat{e}}}
   \newcommand{\fhat}{{\hat{f}}}
   \newcommand{\ghat}{{\hat{g}}}
   \newcommand{\hhat}{{\hat{h}}}
   \newcommand{\ihat}{{\hat{i}}}
   \newcommand{\jhat}{{\hat{j}}}
   \newcommand{\khat}{{\hat{k}}}
   \newcommand{\lhat}{{\hat{l}}}
   \newcommand{\mhat}{{\hat{m}}}
   \newcommand{\nhat}{{\hat{n}}}
   \newcommand{\ohat}{{\hat{o}}}
   \newcommand{\phat}{{\hat{p}}}
   \newcommand{\qhat}{{\hat{q}}}
   \newcommand{\rhat}{{\hat{r}}}
   \newcommand{\shat}{{\hat{s}}}
   \newcommand{\that}{{\hat{t}}}
   \newcommand{\uhat}{{\hat{u}}}
   \newcommand{\vhat}{{\hat{v}}}
   \newcommand{\what}{{\hat{w}}}
   \newcommand{\xhat}{{\hat{x}}}
   \newcommand{\yhat}{{\hat{y}}}
   \newcommand{\zhat}{{\hat{z}}}

\newcommand{\rhohat}{{\hat{\rho}}}
\newcommand{\phihat}{{\hat{\phi}}}
\newcommand{\thetahat}{{\hat{\theta}}}

	\newcommand{\Abar}{{\overline{A}}}
	\newcommand{\Bbar}{{\overline{B}}}
        \newcommand{\Cbar}{{\overline{C}}}
        \newcommand{\Dbar}{{\overline{D}}}
	\newcommand{\Ebar}{{\overline{E}}}
	\newcommand{\Fbar}{{\overline{F}}}
	\newcommand{\Gbar}{{\overline{G}}}
	\newcommand{\Hbar}{{\overline{H}}}
	\newcommand{\Ibar}{{\overline{I}}}
	\newcommand{\Jbar}{{\overline{J}}}
	\newcommand{\Kbar}{{\overline{K}}}
	\newcommand{\Lbar}{{\overline{L}}}
	\newcommand{\Mbar}{{\overline{M}}}
	\newcommand{\Nbar}{{\overline{N}}}
	\newcommand{\Obar}{{\overline{O}}}
	\newcommand{\Pbar}{{\overline{P}}}
	\newcommand{\Qbar}{{\overline{Q}}}
	\newcommand{\Rbar}{{\overline{R}}}
	\newcommand{\Sbar}{{\overline{S}}}
	\newcommand{\Tbar}{{\overline{T}}}
	\newcommand{\Ubar}{{\overline{U}}}
        \newcommand{\Vbar}{{\overline{V}}}	
	\newcommand{\Wbar}{{\overline{W}}}
	\newcommand{\Xbar}{{\overline{X}}}
	\newcommand{\Ybar}{{\overline{Y}}}
        \newcommand{\Zbar}{{\overline{Z}}}
   \newcommand{\abar}{{\bar{a}}}
   \newcommand{\bbar}{{\bar{b}}}
   \newcommand{\cbar}{{\bar{c}}}
   \newcommand{\dbar}{{\bar{d}}}
   \newcommand{\ebar}{{\bar{e}}}
   \newcommand{\fbar}{{\bar{f}}}
   \newcommand{\gbar}{{\bar{g}}}
%   \newcommand{\hbar}{{\bar{h}}} already defined
   \newcommand{\ibar}{{\bar{i}}}
   \newcommand{\jbar}{{\bar{j}}}
   \newcommand{\kbar}{{\bar{k}}}
   \newcommand{\lbar}{{\bar{l}}}
   \newcommand{\mbar}{{\bar{m}}}
   \newcommand{\nbar}{{\bar{n}}}
   \newcommand{\obar}{{\bar{o}}}
   \newcommand{\pbar}{{\bar{p}}}
   \newcommand{\qbar}{{\bar{q}}}
   \newcommand{\rbar}{{\bar{r}}}
   \newcommand{\sbar}{{\bar{s}}}
   \newcommand{\tbar}{{\bar{t}}}
   \newcommand{\ubar}{{\bar{u}}}
   \newcommand{\vbar}{{\bar{v}}}
   \newcommand{\wbar}{{\bar{w}}}
   \newcommand{\xbar}{{\bar{x}}}
   \newcommand{\ybar}{{\bar{y}}}
   \newcommand{\zbar}{{\bar{z}}}
	\newcommand{\Atil}{{\tilde{A}}}
	\newcommand{\Btil}{{\tilde{B}}}
        \newcommand{\Ctil}{{\tilde{C}}}
        \newcommand{\Dtil}{{\tilde{D}}}
	\newcommand{\Etil}{{\tilde{E}}}
	\newcommand{\Ftil}{{\tilde{F}}}
	\newcommand{\Gtil}{{\tilde{G}}}
	\newcommand{\Htil}{{\tilde{H}}}
	\newcommand{\Itil}{{\tilde{I}}}
	\newcommand{\Jtil}{{\tilde{J}}}
	\newcommand{\Ktil}{{\tilde{K}}}
	\newcommand{\Ltil}{{\tilde{L}}}
	\newcommand{\Mtil}{{\tilde{M}}}
	\newcommand{\Ntil}{{\tilde{N}}}
	\newcommand{\Otil}{{\tilde{O}}}
	\newcommand{\Ptil}{{\tilde{P}}}
	\newcommand{\Qtil}{{\tilde{Q}}}
	\newcommand{\Rtil}{{\tilde{R}}}
	\newcommand{\Stil}{{\tilde{S}}}
	\newcommand{\Ttil}{{\tilde{T}}}
	\newcommand{\Util}{{\tilde{U}}}
        \newcommand{\Vtil}{{\tilde{V}}}	
	\newcommand{\Wtil}{{\tilde{W}}}
	\newcommand{\Xtil}{{\tilde{X}}}
	\newcommand{\Ytil}{{\tilde{Y}}}
        \newcommand{\Ztil}{{\tilde{Z}}}
   \newcommand{\atil}{{\tilde{a}}}
   \newcommand{\btil}{{\tilde{b}}}
   \newcommand{\ctil}{{\tilde{c}}}
   \newcommand{\dtil}{{\tilde{d}}}
   \newcommand{\etil}{{\tilde{e}}}
   \newcommand{\ftil}{{\tilde{f}}}
   \newcommand{\gtil}{{\tilde{g}}}
   \newcommand{\htil}{{\tilde{h}}}
   \newcommand{\itil}{{\tilde{i}}}
   \newcommand{\jtil}{{\tilde{j}}}
   \newcommand{\ktil}{{\tilde{k}}}
   \newcommand{\ltil}{{\tilde{l}}}
   \newcommand{\mtil}{{\tilde{m}}}
   \newcommand{\ntil}{{\tilde{n}}}
   \newcommand{\otil}{{\tilde{o}}}
   \newcommand{\ptil}{{\tilde{p}}}
   \newcommand{\qtil}{{\tilde{q}}}
   \newcommand{\rtil}{{\tilde{r}}}
   \newcommand{\stil}{{\tilde{s}}}
   \newcommand{\ttil}{{\tilde{t}}}
   \newcommand{\util}{{\tilde{u}}}
   \newcommand{\vtil}{{\tilde{v}}}
   \newcommand{\wtil}{{\tilde{w}}}
   \newcommand{\xtil}{{\tilde{x}}}
   \newcommand{\ytil}{{\tilde{y}}}
   \newcommand{\ztil}{{\tilde{z}}}

	\newcommand{\headline}[1]{\begin{center}
		{\underline{\bf #1}}\end{center}}
	\newcommand{\centln}[1]{\begin{center} #1 \end{center}}


\newcommand{\column}[1]{\begin{array}{c} #1\end{array}}
\newcommand{\goes}{\rightarrow}
\newcommand{\rarrow}{\mbox{$\longrightarrow$}}
\newcommand{\larrow}{\mbox{$\longleftarrow$}}

% Itemizing Commands
\newcommand{\itemln}[1]{\item[#1] \mbox{ }\\}
\newcommand{\itmbf}[1]{\itm{{\bf #1}\ }}
\newcommand{\itmlabel}[2]{\itm{{\bf #1\ }\topbox{#2}}}
\newcommand{\itembf}[1]{\item {\bf #1}}
\newcommand{\itm}{\medskip\par\noindent$\bullet$\ }
\newcommand{\itmtxt}[1]{\itm {\bf #1:\ }}
\newcommand{\defn}{\itmtxt{Definition}}
\newcommand{\rem}{\itmtxt{Remark}}
%\newcommand{\example}{\itmtxt{Example}}
\newcommand{\claim}{\itmtxt{Claim}}
\newcommand{\proof}{\itmtxt{Proof}}
\newcommand{\limty}[1]{\lim_{#1\rightarrow\infty}}