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\title{Digital lydbehandling}
\author{{\O}yvind Hammer\\ Norsk nettverk for Teknologi, Akustikk og Musikk}
\date{Oslo, \today}


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\samepage \begin{displaymath}f_{1}=\frac{v}{4L}=\frac{343 m/s}{4{\cdot}1.4m}=61 Hz.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=akluk3.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{${\lambda}=\frac{4L}{3}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5867: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}f_{3}=\frac{v}{\frac{4L}{3}}=3f_{1}=184 Hz.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$f_{5}=5f_{1}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5869: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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}

{\newpage
\clearpage
\samepage \begin{displaymath}f_{1}=\frac{v}{4L}=\frac{343 m/s}{4{\cdot}2.4m}=36 Hz.
\end{displaymath}
}

\stepcounter{subsection}
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\samepage \setbox\sizebox=\hbox{$f_{2}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5877: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$f_{4}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5879: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
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\samepage \setbox\sizebox=\hbox{$f_{6}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5881: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\samepage \setbox\sizebox=\hbox{$f_{8}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5885: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$f_{12}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5887: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{displaymath}k=\frac{v}{v+v_{s}} \end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$v_{s}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5899: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

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{\newpage
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\samepage \setbox\sizebox=\hbox{$v_{s}=-v$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5909: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\frac{0.2 m}{343 m/s}=0.6 ms$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5911: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp1.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp2.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp3.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp4.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp5.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{section}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dsp6.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{displaymath}{\cal F}\left[x(t)\sum_{n=-{\infty}}^{\infty}{\delta}(t-nT)\right]
    = X(f){\ast}\left[\sum_{m=-{\infty}}^{\infty}{\delta}(f-mf_{s})\right]
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
\begin{picture}(16,5)
\setlength{\fboxsep}{0.2cm}
\put(0,2.45){Inn}
\put(0.6,2.6){\vector(1,0){0.4}}
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\put(3.5,2.6){\vector(1,0){0.5}}
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\stepcounter{section}
{\newpage
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\samepage \setbox\sizebox=\hbox{$2^{3}=8$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5939: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\frac{8 V}{1 V}{\approx}18 dB.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$2^{8}=256$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5941: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\frac{8 V}{256}=\frac{1}{32} V$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5943: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}\frac{8 V}{\frac{1}{32} V}{\approx}48 dB.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}SN = \frac{A}{\frac{A}{2^{n}}} = 2^{n} {\approx} 6n\;db\;(effekt)
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$SN = (6.02{\cdot}n+1.76) dB$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5949: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{chapter}
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{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$f_{m}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5951: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
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\samepage \setbox\sizebox=\hbox{${\pm}f_{m}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline5953: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}cos(a)cos(b)=\frac{1}{2}{\lbrack}cos(a+b)+cos(a-b){\rbrack}.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlring.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
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{\newpage
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\samepage \begin{figure}[htbp]
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{\newpage
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\samepage \begin{figure}[htbp]
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{\newpage
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\samepage \begin{figure}[htbp]
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{\newpage
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\samepage \begin{figure}[htbp]
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{\newpage
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\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dl2dbes5.ps,height=7cm}}}
  
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}

{\newpage
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\samepage \begin{figure}[htbp]
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\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{displaymath}f(x)=2x \end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}f(x)=abs(x) \end{displaymath}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlchirp.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlchirp16.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlchirp32.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlchirp64.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlmax64.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlpeakd.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$F_{0}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6049: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlks1.ps,height=7.2cm}}}
  
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}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlks2.ps,height=7.2cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlks3.ps,height=7.2cm}}}
  
\end{figure}
}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlfltlp.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlflthp.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlfltbp.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlfltbs.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlfltkam.ps,height=7cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlfltap.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{eqnarray*}y_{n}=a_{1}x_{n}&+&a_{2}x_{n-1}+a_{3}x_{n-2}+ \cdots \\ 
                  &+&b_{2}y_{n-1}+b_{3}y_{n-2}+ \cdots
\end{eqnarray*}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y_{n}=0.5{\cdot}x_{n}+0.5{\cdot}x_{n-1}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlgflt.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{subsection}
{\newpage
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\samepage \setbox\sizebox=\hbox{$2^{10}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6089: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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\samepage \setbox\sizebox=\hbox{$2^{11}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6091: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$F_{s}=32$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6107: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$f=mc^{2}/h$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6115: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=standardheisen.ps,height=8cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=fourierheisen.ps,height=8cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=smallwindowheisen.ps,height=8cm}}}
  
\end{figure}
}

{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=largewindowheisen.ps,height=8cm}}}
  
\end{figure}
}

\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlhanning.ps,height=8cm}}}
  
\end{figure}
}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=dlvosim.ps,height=7cm}}}
  
\end{figure}
}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{figure}[htbp]
  \centerline{\protect\fbox{\psfig{figure=waveletheisen.ps,height=8cm}}}
  
\end{figure}
}

\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{displaymath}y_{n}=x_{n}+x_{n-m}
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}y_{n}=x_{n}+x_{n-m}+d{\cdot}y_{n-m}.
\end{displaymath}
}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$f_i$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6177: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$a_i$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6179: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

{\newpage
\clearpage
\samepage \begin{displaymath}f=\frac{\sum_{i=1}^{N}a_if_i}{\sum_{i=1}^Na_i}.
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}E=-\sum_{i=1}^Na_i{\ln}a_i ,
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\sum a_i=1$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline6185: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
}

\stepcounter{chapter}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage
\clearpage
\samepage \begin{eqnarray*}p1&=&instrumentnummer \nonumber\\ 
p2&=&starttidspunkt   \nonumber\\ 
p3&=&varighet         \nonumber\\ 
\end{eqnarray*}
}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
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\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{chapter}

\end{document}
