In Continuous Time, we use the \emph{Dirac Delta} function. (Technically not a function, and the height is actually infinite)

%\begin{figure}[htp]
%\centering
%\includegraphics{images/dirac/dirac.ps}
%\caption{ The Dirac Delta }
%\label{ fig:dirac }
%\end{figure}

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%  position
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% axes
\psline{->}(-3.428,0)(3.428,0)
\rput(3.428,-0.3){ $t$ }
	
\end{pspicture}
\end{center}

In Discrete Time, we use the \emph{Kronecker Delta} function.

%\begin{figure}[htp]
%\centering
%\includegraphics{images/kronecker.ps}
%\caption{ The Unit Impulse, a.k.a Kronecker Delta }
%\label{ fig:kronecker }
%\end{figure}

\begin{center}
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% line
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%  position
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%  position
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% line
\psline{-*}(0.000,0)(0.000,1)
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\rput(0.25,1){(1)}
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%  position
\rput(2.571,-0.4){3}
% axes
\psline{->}(-3.428,0)(3.428,0)
\rput(3.428,-0.3){ $n$ }
\rput(2.928,1.857){ $\delta(n)$ }
	
\end{pspicture}
\end{center}

The Kronecker Delta function is used in the linear combination:
$$ \sum_{m \in M} x(m) \delta(n-m)  $$

Another signal that we use to decompose signals is the \emph{Complex Exponential}.

This signal is given by

$$ e^{i \theta t};  t \in \R$$ 
$$ e^{i \theta n};  n \in \Z$$ 


Signals to Decompose Signals