View source for Wave Digital Filters applied to the Dunlop "Fuzz Face" Distortion Circuit


== Project Overview ==
Due to recent theoretical developments in "Virtual Analog" and nonlinear physical modeling, many vintage analog effects are now able to be digitized and modeled efficiently within a Wave Digital Filter (WDF) framework. In my project, I plan to brush up on the math behind the new WDF modeling schemes by analyzing the iconic Dunlop "Fuzz Face" distortion pedal through a WDF lens. My goals for the quarter are as follows:

1) Catch up on all of the recent literary developments regarding WDFs.

2) Analyze the particular stages and components of the original analog "Kirchoff" domain circuit in SPICE.

3) Extract the key parameters from the analog components that contribute to the signature tone of the effect.

4) Convert the circuit into a real-time, computable Binary Connection Tree (BCT) WDF model using the new nonlinear modeling techniques.

5) Simulate the WDF version of the circuit using MATLAB and compare to the original version.

6) (if possible) Use the alpha release of the C++ WDF Framework being developed in CCRMA to make a VST plugin of the filter.

== Week 1 ==
I was first introduced to WDF's last year in JOS's physical modeling course: MUSIC 420. I took this week to look over the WDF section in ''Physical Audio Signal Processing'' by Julius Orion Smith III ([http://https://ccrma.stanford.edu/~jos/pasp/Wave_Digital_Filters_I.html])

Below are some of the main takeaways:

1) Every delay element in a WDF can be interpreted physically as holding the current state of a mass or spring (or capacitor or inductor).

2) WDFs are finite-difference schemes that have unusually good numerical properties

3) Voltages and currents (forces and velocities) are viewed in the traveling wave domain instead of the Kirchoff domain.

4) Each circuit component (voltage sources, capacitors, resistors, inductors) has a simple discrete time model in the wave domain. These components are connected using "adaptors" (series or parallel) based on Wave Scattering Theory.

I look forward to reviewing the examples in link provided above to refresh on the properties of WDFs.

== Week 2 ==
After working through some basic examples found in MUSIC 420, I reached out to CCRMA's own Ross Dunkel, who is currently researching WDF applications towards a digital model of the Fender Bassman amplifier. I knew that Ross was working on a standardized C++ library for making WDF-based VST plugins with visiting scholar Maximilian Rest. According to Ross, the framework is almost ready for a local "Alpha" release. I discussed my interest in building a WDF-based VST plugin/audio effect with the framework. Ross suggested the Dunlop Fuzz Face as a prime example to work on.

After selecting my circuit, I asked Ross for some advice on how to incorporate nonlinear elements into a WDF. All of the examples I've covered have only dealt with linear circuit elements in either series or parallel connections.

Ross directed me towards Kurt Werner's (CCRMA) research and other pivotal references below:

-Werner DAFx 2015 ''RESOLVING WAVE DIGITAL FILTERS WITH MULTIPLE/MULTIPORT
NONLINEARITIES''[http://www.ntnu.edu/documents/1001201110/1266017954/DAFx-15_submission_54.pdf/f8958bcb-ee0a-4be4-b741-f7297f49cf40]

-Werner DAFx 2015 ''WAVE DIGITAL FILTER ADAPTORS FOR ARBITRARY TOPOLOGIES AND MULTIPORT
LINEAR ELEMENTS'' [http://www.ntnu.edu/documents/1001201110/1266017954/DAFx-15_submission_53.pdf/a559ce90-d16b-49a3-a267-5b877d7fe70b]

-Werner WASPAA 2015 [http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7336908&tag=1]

-de Sanctis and Sarti Virtual Analog 2010 [http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5276845]

== Week 3 ==
In order to digitize the Fuzz Face, I reviewed all of the stages of the analog circuit. Due to its characteristic tone and historical significance, there are many web pages devoted to the analysis of the circuit. These are the two most informative.

1) Electrosmash Fuzz Face Analysis [http://www.electrosmash.com/fuzz-face]

2) Geofex [http://www.geofex.com/article_folders/fuzzface/fffram.htm]

The circuit is a two stage amplifier with a feedback stage. The feedback network holds all of the important characteristics.

[http://www.electrosmash.com/images/tech/fuzz-face/fuzz-face-original-schematic-parts.png FuzzFace Schematic]

According to various sources (including the ones linked above), the FuzzFace's signature tone comes from its use of the matched pair of AC128 NPN Germanium Transistors. Commonly accepted to produce a smoother and less harsh tone than the more reliable silicon counterparts, the AC128's have a shorter lifespan and their parameters can vary drastically from component to component. These transistors, however, are key to achieving the asymmetric clipping at medium gains, which is the most iconic tone of the FuzzFace (featured in many Jimi Hendrix guitar solos)

Ideally, I need to search for 2 AC128 transistors with particular current gains (Beta parameter) to achieve the sought-after old school tone. Referred to as a "matched pair," it is good to have Q1 with Beta = 70-80 and a Q2 with Beta = 110-130.

== Week 4 ==
To get a feel for the FuzzFace circuit characteristics, it's DC bias points, frequency response, etc, I decided to put together an early stage simulation in LTSPICE. The following link contains a screenshot of the SPICE schematic of this early stage simulation

[https://stanford.box.com/s/r5fjjjckuik6bdylecw4iq235t2moa3c FuzzFace SPICE Schematic Version 1]

Below is an input-output graph (in the time domain and frequency domain) for sine tone at 440 Hz.

[https://stanford.box.com/s/udnmoxilu9w1fd2lim6okf837h2xyyky Time Domain Input-Output]