6.tex

\textbf{Class notes: Jan 12, 2016}

Notes for Paul:

- Make a "notes for paul" latex macro

- Learn more about the S-Plane and Z-plane (we will be doing both in this class 
simultaneously)

- Faust filters: many of them are just an impulse sent through a 2nd order filter

- df-1 and df-2 differ by whether or not the zeroes come first or second

\josquote{There is a rate of evaporation of hardware in this vacinity}

\subsection*{Direct Form Filters}

\josquote{Truth is Truth.}

% https://ccrma.stanford.edu/~jos/fp/Direct_Form_I.html

Difference equation: Discrete form of differential equation

- takes a linear combination of the current input, and the past inputs

- can't see the future: causal

- Show up in the numerator of the transfer function

- if it's an FIR, b cf are the impulse response

- vector 'b', sequence of b's, followed by zeros

- TODO: try to see this in terms of convolution (connect it, "last quarters way of thinking about this")

- "running linear combination

- 2 points = two point smoother, running 2 point sum filter

- b-part is only the FIR part, no feedback

- feedback is new this quarter: coudln't do it last semester because the IR is infinite

\textit{(there should definitely be a sidenote thingy for meanderings...
How does one "chart" this lecture?
)} 

- some ways to  model reverbation: ray tracing boundary modelling

\josquote{The gaming industry drives this stuff.}

- impulse response is only accurate for a fixed point fixed source fixed geometry

- reverb is trying to come from everywhere at once

- diffuse field

- image method reverberation: take your room, replicate it. 

- the walls are suddenly made out of mirrors, and you clap: imagine where you'll see those pair of hands. you'll see the hands in 
6 places at first, but you'll realize there are an infinite amount of hands. 

- dual of image method: trakcing a spherical wave that gvoes out when you clap your hands. let it go through
the walls. Find the sound field by adding all the rooms that the soudn wave is in.

-infinite honey comb of image rooms, spherical wave that expands out. take all teh rooms intersecting the sphere 
at that time, and add them together. You'll get a lot of near plane waves, one from every direction. Timing is random
phase is random.

- late in the reverb: diffuse. 

\josquote{You don't localize reverb, you swim in it.} 

- The "diffuse snow field"

\textit{Now were talking about snow clearing infrastructure in Helsinki}

- Impulse response in an ice hotel \\