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wdmodels.lib
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//#################################### wdmodels.lib ##############################################################################
// A library of basic adaptors and methods to help construct Wave Digital Filter models in Faust. Its official prefix is `wd`.
// ## Library Readme
// This library is intended for use for creating Wave Digital (WD) based models of audio circuitry for real-time audio processing within the Faust programming language. The goal is to provide a framework to create real-time virtual-analog audio effects and synthesizers using WD models without the use of C++. Furthermore, we seek to provide access to the technique of WD modeling to those without extensive knowledge of advanced digital signal processing techniques. Finally, we hope to provide a library which can integrate with all aspects of Faust, thus creating a platform for virtual circuit bending.
// The library itself is written in Faust to maintain portability.
//
// This library is heavily based on Kurt Werner's Dissertation, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters." I have tried to maintain consistent notation between the adaptors appearing within thesis and my adaptor code. The majority of the adaptors found in chapter 1 and chapter 3 are currently supported.
//
// For inquires about use of this library in a commercial product, please contact dirk [dot] roosenburg [dot] 30 [at] gmail [dot] com.
// This documentation is taken directly from the [readme](https://github.com/droosenb/faust-wdf-library). Please refer to it for a more updated version.
//
// Many of the more in depth comments within the library include jargon. I plan to create videos detailing the theory of WD models.
// For now I recommend Kurt Werner's PhD, [Virtual analog modeling of Audio circuitry using Wave Digital Filters](https://searchworks.stanford.edu/view/11891203).
// I have tried to maintain consistent syntax and notation to the thesis.
// This library currently includes the majority of the adaptors covered in chapter 1 and some from chapter 3.
//
//
// ## Using this Library
//
// Use of this library expects some level of familiarity with WDF techniques, especially simplification and decomposition of electronic circuits into WDF connection trees. I plan to create video to cover both these techniques and use of the library.
//
// ### Quick Start
//
// To get a quick overview of the library, start with the `secondOrderFilters.dsp` code found in [examples](https://github.com/droosenb/faust-wdf-library/tree/main/examples).
// Note that the `wdmodels.lib` library is now embedded in the [online Faust IDE](https://faustide.grame.fr/).
//
// ### A Simple RC Filter Model
//
// Creating a model using this library consists fo three steps. First, declare a set of components.
// Second, model the relationship between them using a tree. Finally, build the tree using the libraries build functions.
//
// First, a set of components is declared using adaptors from the library.
// This list of components is created based on analysis of the circuit using WDF techniques,
// though generally each circuit element (resistor, capacitor, diode, etc.) can be expected to appear
// within the component set. For example, first order RC lowpass filter would require an unadapted voltage source,
// a 47k resistor, and a 10nF capacitor which outputs the voltage across itself. These can be declared with:
//
// ```
// vs1(i) = wd.u_voltage(i, no.noise);
// r1(i) = wd.resistor(i, 47*10^3);
// c1(i) = wd.capacitor_Vout(i, 10*10^-9);
// ```
//
// Note that the first argument, i, is left un-parametrized. Components must be declared in this form, as the build algorithm expects to receive adaptors which have exactly one parameter.
//
// Also note that we have chosen to declare a white noise function as the input to our voltage source.
// We could potentially declare this as a direct input to our model, but to do so is more complicated
// process which cannot be covered within this tutorial. For information on how to do this see
// [Declaring Model Parameters as Inputs](#declaring-model-parameters-as-inputs) or see various implementations
// in [examples](https://github.com/droosenb/faust-wdf-library/tree/main/examples).
//
// Second, the declared components and interconnection/structural adaptors (i.e. series, parallel, etc) are arranged
// into the connection tree which is produced from performing WD analysis on the modeled circuit.
// For example, to produce our first order RC lowpass circuit model, the following tree is declared:
//
// `tree_lowpass = vs1 : wd.series : (r1, c1);`
//
// For more information on how to represent trees in Faust, see [Trees in Faust](#trees-in-faust).
//
// Finally, the tree is built using the the `buildtree` function. To build and compute our first order
// RC lowpass circuit model, we use:
//
// `process = wd.buildtree(tree_lowpass);`
//
// More information about build functions, see [Model Building Functions](#model-building-functions).
//
// ### Building a Model
//
// After creating a connection tree which consists of WD adaptors, the connection tree must be passed
// to a build function in order to build the model.
//
// ##### Automatic model building
//
// `buildtree(connection_tree)`
//
// The simplest build function for use with basic models. This automatically implements `buildup`, `builddown`,
// and `buildout` to create a working model. However, it gives minimum control to the user and cannot
// currently be used on trees which have parameters declared as inputs.
//
// ##### Manual model building
//
// Wave Digital Filters are an explicit state-space model, meaning they use a previous system state
// in order to calculate the current output. This is achieved in Faust by using a single global feedback operator.
// The models feed-forward terms are generated using `builddown` and the models feedback terms are generated
// using `buildup`. Thus, the most common model implementation (the method used by `buildtree`) is:
//
// `builddown(connection_tree)~buildup(connection_tree) : buildout(connection_tree)`
//
// Since the `~` operator in Faust will leave feedback terms hanging as outputs, `buildout` is a function provided for convenience.
// It automatically truncates the hanging outputs by identifying leaf components which have an intended output
// and generating an output matrix.
//
// Building the model manually allows for greater user control and is often very helpful in testing.
// Also provided for testing are the `getres` and `parres` functions, which can be used to determine
// the upward-facing port resistance of an element.
//
// ### Declaring Model Parameters as Inputs
//
// When possible, parameters of components should be declared explicitly, meaning they are dependent on a function with no inputs.
// This might be something as simple as integer(declaring a static component), a function dependent on a UI input (declaring a component with variable value),
// or even a time-dependent function like an oscillator (declaring an audio input or circuit bending).
//
// However, it is often necessary to declare parameters as input. To achieve this there are two possible methods.
// The first and recommended option is to create a separate model function and declare parameters which will later
// be implemented as inputs. This allows inputs to be explicitly declared as component parameters.
// For example, one might use:
//
// ```
// model(in1) = buildtree(tree)
// with {
// ...
// vin(i) = wd.u_voltage(i, in1);
// ...
// tree = vin : ...;
// };
// ```
//
// In order to simulate an audio input to the circuit.
//
// Note that the tree and components must be declared inside a `with {...}` statement, or the model's parameters will not be accessible.
//
// ##### The Empty Signal Operator
//
// The Empty signal operator, `_` should NEVER be used to declare a parameter as in input in a wave-digital model.
//
// Using it will result on breaking the internal routing of the model and thus breaks the model.
// Instead, use explicit declaration as shown directly above.
//
// ### Trees in Faust
//
// Since WD models use connection trees to represent relationships of elements, a comprehensive way to represent trees is critical.
// As there is no current convention for creating trees in Faust, I've developed a method using the existing series and parallel/list
// methods in Faust.
//
// The series operator ` : ` is used to separate parent and child elements. For example the tree:
//
// ```
// A
// |
// B
// ```
//
// is represented by `A : B` in Faust.
//
// To denote a parent element with multiple child elements, simply use a list `(a1, a2, ... an)` of children connected to a single parent. `
// For example the tree:
//
// ```
// A
// / \
// B C
//
// ```
// is represented by:
//
// `A : (B, C)`
//
// Finally, for a tree with many levels, simply break the tree into subtrees following the above rules and connect
// the subtree as if it was an individual node. For example the tree:
//
// ```
// A
// / \
// B C
// / / \
// X Y Z
// ```
//
// can be represented by:
//
// ```
// B_sub = B : X; //B subtree
// C_sub = C : (Y, Z); //C subtree
// tree = A : (B_sub, C_sub); //full tree
// ```
//
// or more simply, using parentheses:
//
// `A : ((B : X), (C : (Y, Z)))`
// ### How Adaptors are Structured
// In wave digital filters, adaptors can be described by the form `b = Sa` where `b` is a vector of output waves `b = (b0, b1, b2, ... bn)`, `a` is a vector of input waves`a = (a0, a1, a2, ... an)`, and `S` is an n x n scattering matrix.
// `S` is dependent on `R`, a list of port resistances `(R0, R1, R2, ... Rn)`.
//
// The output wave vector `b` can be divided into downward-going and upward-going waves
// (downward-going waves travel down the connection tree, upward-going waves travel up).
// For adapted adaptors, with the zeroth port being the upward-facing port, the downward-going wave vector is `(b1, b2, ... bn)` and the upward-going wave vector is `(b0)`.
// For unadapted adaptors, there are no upward-going waves, so the downward-going wave vector is simply `b = (b0, b1, b2, ... bn)`.
//
// In order for adaptors to be interpretable by the compiler, they must be structured in a specific way.
// Each adaptor is divided into three cases by their first parameter. This parameter, while accessible by the user, should only be set by the compiler/builder.
//
// All other parameters are value declarations (for components), inputs (for voltage or current ins), or parameter controls (for potentiometers/variable capacitors/variable inductors).
//
// ##### First case - downward going waves
//
// `(0, params) => downward-going(R1, ... Rn, a0, a1, ... an)`
// outputs: `(b1, b2, ... bn)`
// this function takes any number of port resistances, the downward going wave, and any number of upward going waves as inputs.
// These values/waves are used to calculate the downward going waves coming from this adaptor.
//
// ##### Second case
//
// `(1, params) => upward-going(R1, ... Rn, a1, ... an)`
// outputs : `(b0)`
// this function takes any number of port resistances and any number of upward going waves as inputs.
// These values/waves are used to calculate the upward going wave coming from this adaptor.
//
// ##### Third case
//
// `(2, params) => port-resistance(R1, ... Rn)`
// outputs: `(R0)`
// this function takes any number of port resistances as inputs.
// These values are used to calculate the upward going port resistance of the element.
//
// ##### Unadapted Adaptors
//
// Unadapted adaptor's names will always begin `u_`
// An unadapted adaptor MUST be used as the root of the WD connection tree.
// Unadapted adaptors can ONLY be used as a root of the WD connection tree.
// While unadapted adaptors contain all three cases, the second and third are purely structural.
// Only the first case should contain computational information.
//
// ### How the Build Functions Work
//
// Expect this section to be added soon! It's currently in progress.
//
// ### Acknowledgements
//
// Many thanks to Kurt Werner for helping me to understand wave digital filter models. Without his publications and consultations, the library would not exist.
// Thanks also to my advisors, Rob Owen and Eli Stine whose input was critical to the development of the library.
// Finally, thanks to Romain Michon, Stephane Letz, and the Faust Slack for contributing to testing, development, and inspiration when creating the library.
//
// #### References
// * <https://github.com/grame-cncm/faustlibraries/blob/master/wdmodels.lib>
//################################################################################################################################
ba = library("basics.lib");
ro = library("routes.lib");
ma = library("maths.lib");
si = library("signals.lib");
declare name "Faust Wave Digital Model Library";
declare version "1.2.1";
//=============================Algebraic One Port Adaptors=================================
//=========================================================================================
//----------------------`(wd.)resistor`--------------------------
// Adapted Resistor.
//
// A basic node implementing a resistor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
//
// #### Usage
//
// ```
// r1(i) = resistor(i, R);
// buildtree( A : r1 );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Resistance/Impedance of the resistor being modeled in Ohms.
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.1
//----------------------------------------------------------
declare resistor author "Dirk Roosenburg";
declare resistor copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resistor license "MIT-style STK-4.3 license";
resistor =
case{
(0, R) => !, 0;
(1, R) => _;
(2, R) => R0
with{
R0 = R;
};
};
//----------------------`(wd.)resistor_Vout`--------------------------
// Adapted Resistor + voltage Out.
//
// A basic adaptor implementing a resistor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// The resistor will also pass the voltage across itself as an output of the model.
//
// #### Usage
//
// ```
// rout(i) = resistor_Vout(i, R);
// buildtree( A : rout ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Resistance/Impedance of the resistor being modeled in Ohms.
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.1
//----------------------------------------------------------
declare resistor_Vout author "Dirk Roosenburg";
declare resistor_Vout copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resistor_Vout license "MIT-style STK-4.3 license";
resistor_Vout =
case{
(0, R) => 0, _*.5;
(1, R) => _, !;
(2, R) => R0
with{
R0 = R;
};
}with{
rho = 1;
};
//----------------------`(wd.)resistor_Iout`--------------------------
// Resistor + current Out.
//
// A basic adaptor implementing a resistor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// The resistor will also pass the current through itself as an output of the model.
//
// #### Usage
//
// ```
// rout(i) = resistor_Iout(i, R);
// buildtree( A : rout ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Resistance/Impedance of the resistor being modeled in Ohms.
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.1
//----------------------------------------------------------
declare resistor_Iout author "Dirk Roosenburg";
declare resistor_Iout copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resistor_Iout license "MIT-style STK-4.3 license";
resistor_Iout =
case{
(0, R) => 0, _*.5/R;
(1, R) => _, !;
(2, R) => R0
with{
R0 = R;
};
};
//----------------------`(wd.)u_voltage`--------------------------
// Unadapted Ideal Voltage Source.
//
// An adaptor implementing an ideal voltage source within Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
// Can be used for either DC (constant) or AC (signal) voltage sources.
//
// #### Usage
//
// ```
// v1(i) = u_Voltage(i, ein);
// buildtree( v1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `ein` : Voltage/Potential across ideal voltage source in Volts
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.2
//----------------------------------------------------------
declare u_voltage author "Dirk Roosenburg";
declare u_voltage copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_voltage license "MIT-style STK-4.3 license";
u_voltage =
case{
(0 , ein) => b0
with{
b0(R0, a0) = 2*R0^(rho-1)*ein -a0;
};
(1, ein) => !, !;
(2, ein) => 0;
}with{
rho = 1;
};
//----------------------`(wd.)u_current`--------------------------
// Unadapted Ideal Current Source.
//
// An unadapted adaptor implementing an ideal current source within Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
// Can be used for either DC (constant) or AC (signal) current sources.
//
// #### Usage
//
// ```
// i1(i) = u_current(i, jin);
// buildtree( i1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `jin` : Current through the ideal current source in Amps
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.3
//----------------------------------------------------------
declare u_current author "Dirk Roosenburg";
declare u_current copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_current license "MIT-style STK-4.3 license";
u_current =
case{
(0 , jin) => b0
with{
b0(R0, a0) = 2*R0^(rho)*jin + a0;
};
(1, jin) => !, !;
(2, jin) => 0;
}with{
rho = 1;
};
//----------------------`(wd.)resVoltage`--------------------------
// Adapted Resistive Voltage Source.
//
// An adaptor implementing a resistive voltage source within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// It is comprised of an ideal voltage source in series with a resistor.
// Can be used for either DC (constant) or AC (signal) voltage sources.
//
// #### Usage
//
// ```
// v1(i) = resVoltage(i, R, ein);
// buildtree( A : v1 );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Resistance/Impedance of the series resistor in Ohms
// * `ein` : Voltage/Potential of the ideal voltage source in Volts
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.4
//----------------------------------------------------------
declare resVoltage author "Dirk Roosenburg";
declare resVoltage copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resVoltage license "MIT-style STK-4.3 license";
resVoltage =
case{
(0, R, ein) => !, R^(1-rho)*ein;
(1, R, ein) => _;
(2, R, ein) => R0
with {
R0 = R;
};
}with{
rho = 1;
};
//----------------------`(wd.)resVoltage_Vout`--------------------------
// Adapted Resistive Voltage Source + voltage output.
//
// An adaptor implementing an adapted resistive voltage source within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// It is comprised of an ideal voltage source in series with a resistor.
// Can be used for either DC (constant) or AC (signal) voltage sources.
// The resistive voltage source will also pass the voltage across it as an output of the model.
//
// #### Usage
//
// ```
// vout(i) = resVoltage_Vout(i, R, ein);
// buildtree( A : vout ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Resistance/Impedance of the series resistor in Ohms
// * `ein` : Voltage/Potential across ideal voltage source in Volts
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.4
//----------------------------------------------------------
declare resVoltage_Vout author "Dirk Roosenburg";
declare resVoltage_Vout copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resVoltage_Vout license "MIT-style STK-4.3 license";
resVoltage_Vout =
case{
(0, R, ein) => R^(1-rho)*ein, _*.5 + R^(1-rho)*ein*.5;
(1, R, ein) => _, !;
(2, R, ein) => R0
with {
R0 = R;
};
}with{
rho = 1;
};
//----------------------`(wd.)u_resVoltage`--------------------------
// Unadapted Resistive Voltage Source.
//
// An unadapted adaptor implementing a resistive voltage source within Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
// It is comprised of an ideal voltage source in series with a resistor.
// Can be used for either DC (constant) or AC (signal) voltage sources.
//
// #### Usage
//
// ```
// v1(i) = u_resVoltage(i, R, ein);
// buildtree( v1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Resistance/Impedance of the series resistor in Ohms
// * `ein` : Voltage/Potential across ideal voltage source in Volts
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.4
//----------------------------------------------------------
declare u_resVoltage author "Dirk Roosenburg";
declare u_resVoltage copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_resVoltage license "MIT-style STK-4.3 license";
u_resVoltage =
case {
(0, R, ein) => b0
with{
b0(R0, a0) = a0*(R - R0)/(R+R0) + ein*(2*R0^rho)/(R + R0);
};
(1, R, ein) => !, !;
(2, R, ein) => 0;
}with{
rho = 1;
};
//----------------------`(wd.)resCurrent`--------------------------
// Adapted Resistive Current Source.
//
// An adaptor implementing a resistive current source within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// It is comprised of an ideal current source in parallel with a resistor.
// Can be used for either DC (constant) or AC (signal) current sources.
//
// #### Usage
//
// ```
// i1(i) = resCurrent(i, R, jin);
// buildtree( A : i1 );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Resistance/Impedance of the parallel resistor in Ohms
// * `jin` : Current through the ideal current source in Amps
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.5
//----------------------------------------------------------
declare resCurrent author "Dirk Roosenburg";
declare resCurrent copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare resCurrent license "MIT-style STK-4.3 license";
resCurrent =
case {
(0, R, jin) => !, R^(rho)*jin;
(1, R, jin) => _;
(2, R, jin) => R0
with {
R0 = R;
};
}with{
rho = 1; //assume voltage waves
};
//----------------------`(wd.)u_resCurrent`--------------------------
// Unadapted Resistive Current Source.
//
// An unadapted adaptor implementing a resistive current source within Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
// It is comprised of an ideal current source in parallel with a resistor.
// Can be used for either DC (constant) or AC (signal) current sources.
//
// #### Usage
//
// ```
// i1(i) = u_resCurrent(i, R, jin);
// buildtree( i1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Resistance/Impedance of the series resistor in Ohms
// * `jin` : Current through the ideal current source in Amps
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.5
//----------------------------------------------------------
declare u_resCurrent author "Dirk Roosenburg";
declare u_resCurrent copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_resCurrent license "MIT-style STK-4.3 license";
u_resCurrent =
case {
(0, R, jin) => b0
with{
b0(R0, a0) = a0*(R - R0)/(R + R0) + jin*(2*R*R0^rho)/(R + R0);
};
(1, R, jin) => !, !;
(2, R, jin) => 0;
}with{
rho = 1; //assume voltage waves
};
//TODO
//add short circuit (1.2.6), add open circuit (1.2.7)
//----------------------`(wd.)u_switch`--------------------------
// Unadapted Ideal Switch.
//
// An unadapted adaptor implementing an ideal switch for Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree
//
// #### Usage
//
// ```
// s1(i) = u_resCurrent(i, lambda);
// buildtree( s1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `lambda` : switch state control. -1 for closed switch, 1 for open switch.
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.2.8
//----------------------------------------------------------
declare u_switch author "Dirk Roosenburg";
declare u_switch copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_switch license "MIT-style STK-4.3 license";
u_switch =
case {
(0, lambda) => b0
with{
b0(R0, a0) = a0*lambda;
};
(1, lambda) => !, !;
(2, lambda) => 0;
};
//=============================Reactive One Port Adaptors=================================
//========================================================================================
//TODO - add mobius transform and alpha transform digitizations
//----------------------`(wd.)capacitor`--------------------------
// Adapted Capacitor.
//
// A basic adaptor implementing a capacitor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// This capacitor model was digitized using the bi-linear transform.
//
// #### Usage
//
// ```
// c1(i) = capacitor(i, R);
// buildtree( A : c1 ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared.
// * `R` : Capacitance/Impedance of the capacitor being modeled in Farads.
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.3.1
//----------------------------------------------------------
declare capacitor author "Dirk Roosenburg";
declare capacitor copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare capacitor license "MIT-style STK-4.3 license";
capacitor =
case{
(0, R) => _*1;
(1, R) => _;
(2, R) => R0
with {
R0 = t/(2*R);
};
}with{
t = 1/ma.SR; //sampling interval
};
//----------------------`(wd.)capacitor_Vout`--------------------------
// Adapted Capacitor + voltage out.
//
// A basic adaptor implementing a capacitor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// The capacitor will also pass the voltage across itself as an output of the model.
// This capacitor model was digitized using the bi-linear transform.
//
// #### Usage
//
// ```
// cout(i) = capacitor_Vout(i, R);
// buildtree( A : cout ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Capacitance/Impedence of the capacitor being modeled in Farads
//
// Note: the adaptor must be declared as a seperate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.3.1
//----------------------------------------------------------
declare capacitor_Vout author "Dirk Roosenburg";
declare capacitor_Vout copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare capacitor_Vout license "MIT-style STK-4.3 license";
capacitor_Vout =
case{
(0, R) => b0
with{
b0(a1) = a1*1, a1*.5 + (a1')*.5;
};
(1, R) => _, !;
(2, R) => R0
with {
R0 = t/(2*R);
};
}with{
t = 1/ma.SR; //sampling interval
};
//----------------------`(wd.)inductor`--------------------------
// Unadapted Inductor.
//
// A basic adaptor implementing an inductor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// This inductor model was digitized using the bi-linear transform.
//
// #### Usage
//
// ```
// l1(i) = inductor(i, R);
// buildtree( A : l1 );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Inductance/Impedance of the inductor being modeled in Henries
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.3.2
//----------------------------------------------------------
declare inductor author "Dirk Roosenburg";
declare inductor copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare inductor license "MIT-style STK-4.3 license";
inductor =
case{
(0, R) => _*(-1);
(1, R) => _;
(2, R) => R0
with {
R0 = (2*R)/t;
};
}with{
t = 1/ma.SR; //sampling interval
};
//----------------------`(wd.)inductor_Vout`--------------------------
// Unadapted Inductor + Voltage out.
//
// A basic adaptor implementing an inductor for use within Wave Digital Filter connection trees.
//
// It should be used as a leaf/terminating element of the connection tree.
// The inductor will also pass the voltage across itself as an output of the model.
// This inductor model was digitized using the bi-linear transform.
//
// #### Usage
//
// ```
// lout(i) = inductor_Vout(i, R);
// buildtree( A : lout ) : _
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `R` : Inductance/Impedance of the inductor being modeled in Henries
//
// Note: the adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 1.3.2
//----------------------------------------------------------
declare inductor_Vout author "Dirk Roosenburg";
declare inductor_Vout copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare inductor_Vout license "MIT-style STK-4.3 license";
inductor_Vout =
case{
(0, R) => b0
with{
b0(a1) = a1*(-1), a1*.5 - (a1')*.5;
};
(1, R) => _, !;
(2, R) => R0
with {
R0 = (2*R)/t;
};
}with{
t = 1/ma.SR; //sampling interval
};
//===============================Nonlinear One Port Adaptors==============================
//========================================================================================
//----------------------`(wd.)u_idealDiode`--------------------------
// Unadapted Ideal Diode.
//
// An unadapted adaptor implementing an ideal diode for Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
//
// #### Usage
//
// ```
// buildtree( u_idealDiode : B );
// ```
//
// Note: only usable as the root of a tree.
// Correct implementation is shown above.
//
// #### Reference
//
// K. Werner, "Virtual Analog Modeling of Audio Circuitry Using Wave Digital Filters", 3.2.3
//----------------------------------------------------------
declare u_idealDiode author "Dirk Roosenburg";
declare u_idealDiode copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_idealDiode license "MIT-style STK-4.3 license";
u_idealDiode =
case{
(0) => b1
with{
b1(R1, a0) = a0 : abs : *(-1);
};
(1) => !, !;
(2) => 0;
};
//----------------------`(wd.)u_chua`--------------------------
// Unadapted Chua Diode.
//
// An adaptor implementing the chua diode / non-linear resistor within Wave Digital Filter connection trees.
//
// It should be used as the root/top element of the connection tree.
//
// #### Usage
//
// ```
// chua1(i) = u_chua(i, G1, G2, V0);
// buildtree( chua1 : B );
// ```
//
// Where:
//
// * `i`: index used by model-building functions. Should never be user declared
// * `G1` : resistance parameter 1 of the chua diode
// * `G2` : resistance parameter 2 of the chua diode
// * `V0` : voltage parameter of the chua diode
//
// Note: only usable as the root of a tree.
// The adaptor must be declared as a separate function before integration into the connection tree.
// Correct implementation is shown above.
//
// #### Reference
//
// Meerkotter and Scholz, "Digital Simulation of Nonlinear Circuits by Wave Digital Filter Principles"
//----------------------------------------------------------
declare u_chua author "Dirk Roosenburg";
declare u_chua copyright "Copyright (C) 2020 by Dirk Roosenburg <[email protected]>";
declare u_chua license "MIT-style STK-4.3 license";
u_chua =
case{
(0, G1, G2, V0) => b1
with{
b1(R1, a0) = g_1*a0 + 1/2*(g_2 - g_1)*(((a0 + a_0) : abs) - ((a0 - a_0): abs))
with{
g_1 = (1-G1*R1)/(1+G1*R1);
g_2 = (1-G2*R1)/(1+G2*R1);
a_0 = V0*(1+G2*R1);
};
};
(1, G1, G2, V0) => !, !;
(2, G1, G2, V0) => 0;
};
//----------------------`(wd.)lambert`--------------------------
// An implementation of the lambert function.
// It uses Halley's method of iteration to approximate the output.
// Included in the WD library for use in non-linear diode models.