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{\Large \textbf{Representation of Signals}}\\
Don H. Johnson\\
\today
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In simple terms, a signal $\signal{t}$ can be decomposed as a superposition---a sum---of simpler signals in most cases of interest.
In particular, we can define a \emph{basis} as a family of functions
$\{\phi_k(\cdot)\}$ that represents a signal according to
\[
\signal{t} = \sum_{k=1}^{\infty} a_k\phi_k(t)\; ,
\]
where, finally, $\{a_k\}$ is a sequence of scalars defined both by the basis and the signal.
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