21.tex

video notes: 13.mp4


\subsection*{Quality Factor (Q)}
\begin{itemize}

\item{No relation to the Q continuum.}

\item{
It pertains to resonators:
}

\item{resonance freq / bandwidth is Q}

\item{S-plane is a good respresenation}
\item{The simplest resonator is just a single pole, with a 
real/imaginary part}
\item{$\sigma_p < 0$ if they are to be stable}
\item{RC (resistor-capacitor) filter: has exponential decay for it's IR}
\item{If you make an inductor and capacitor in a circuit, you'll get a 
resonator... but we haven't derived this yet}
\item{\textit{Network synthesis}: taking an arbitrary s-plane transfer function and seeing it in 
various forms}
\item{For us, it's best to see all the ways to get back to the z-plane and get
a discrete time implemenation.}
\item{Let's be discrete: hearing is finite: we can only hear so much dynamic range, bandwidth}
\item{$H(s) = \frac{1}{s - p}$}
\item{She's gone, Jim...}
\end{itemize}