signals - Faust Libraries

# signals.lib

A library of basic elements to handle signals in Faust. Its official prefix is `si`.

#### References

- https://github.com/grame-cncm/faustlibraries/blob/master/signals.lib

## Functions Reference

### `(si.)bus`

Put N cables in parallel. `bus` is a standard Faust function.

#### Usage

    bus(N)
    bus(4) : _,_,_,_

Where:

- `N`: is an integer known at compile time that indicates the number of parallel cables

### `(si.)block`

Block - terminate N signals. `block` is a standard Faust function.

#### Usage

    si.bus(N) : block(N)

Where:

- `N`: the number of signals to be blocked known at compile time

### `(si.)interpolate`

Linear interpolation between two signals.

#### Usage

    _,_ : interpolate(i) : _

Where:

- `i`: interpolation control between 0 and 1 (0: first input; 1: second input)

### `(si.)repeat`

Repeat an effect N time(s) and take the parallel sum of all intermediate buses.

#### References

- https://github.com/orlarey/presentation-compilateur-faust/blob/master/slides.pdf

#### Usage

    si.bus(inputs(FX)) : repeat(N, FX) : si.bus(outputs(FX))

Where:

- `N`: Number of repetitions, minimum of 1, a constant numerical expression
- `FX`: an arbitrary effect (N inputs and N outputs) that will be repeated

Example 1:

    process = repeat(2, dm.zita_light) : _*.5,_*.5;

Example 2:

    N = 4;
    C = 2;
    fx(i) = i+1, par(j, C, @(i*5000));
    process = 0, si.bus(C) : repeat(N, fx) : !, par(i, C, _*.2/N);

### `(si.)smoo`

Smoothing function based on `smooth` ideal to smooth UI signals (sliders, etc.) down. Approximately, this is a 7 Hz one-pole low-pass considering the coefficient calculation: exp(-2pi*CF/SR).

`smoo` is a standard Faust function.

#### Usage

    hslider(...) : smoo;

### `(si.)polySmooth`

A smoothing function based on `smooth` that doesn't smooth when a trigger signal is given. This is very useful when making polyphonic synthesizer to make sure that the value of the parameter is the right one when the note is started.

#### Usage

    hslider(...) : polySmooth(g,s,d) : _

Where:

- `g`: the gate/trigger signal used when making polyphonic synths
- `s`: the smoothness (see `smooth`)
- `d`: the number of samples to wait before the signal start being smoothed after `g` switched to 1

### `(si.)smoothAndH`

A smoothing function based on `smooth` that holds its output signal when a trigger is sent to it. This feature is convenient when implementing polyphonic instruments to prevent some smoothed parameter to change when a note-off event is sent.

#### Usage

    hslider(...) : smoothAndH(g,s) : _

Where:

- `g`: the hold signal (0 for hold, 1 for bypass)
- `s`: the smoothness (see `smooth`)

### `(si.)bsmooth`

Block smooth linear interpolation during a block of samples (given by the `ma.BS` value).

#### Usage

    hslider(...) : bsmooth : _

### `(si.)dot`

Dot product for two vectors of size N.

#### Usage

    si.bus(N), si.bus(N) : dot(N) : _

Where:

- `N`: size of the vectors (int, must be known at compile time)

### `(si.)smooth`

Exponential smoothing by a unity-dc-gain one-pole lowpass. `smooth` is a standard Faust function.

#### Usage:

    _ : si.smooth(ba.tau2pole(tau)) : _

Where:

- `tau`: desired smoothing time constant in seconds, or

    hslider(...) : smooth(s) : _

Where:

- `s`: smoothness between 0 and 1. s=0 for no smoothing, s=0.999 is "very smooth", s>1 is unstable, and s=1 yields the zero signal for all inputs. The exponential time-constant is approximately 1/(1-s) samples, when s is close to (but less than) 1.

#### References:

- https://ccrma.stanford.edu/~jos/mdft/Convolution_Example_2_ADSR.html
- https://ccrma.stanford.edu/~jos/aspf/Appendix_B_Inspecting_Assembly.html

### `(si.)smoothq`

Smoothing with continuously variable curves from Exponential to Linear, with a constant time.

#### Usage

    _ : smoothq(time, q) : _;

Where:

- `time`: seconds to reach target
- `q`: curve shape (between 0..1, 0 is Exponential, 1 is Linear)

### `(si.)cbus`

N parallel cables for complex signals. `cbus` is a standard Faust function.

#### Usage

    cbus(N)
    cbus(4) : (r0,i0), (r1,i1), (r2,i2), (r3,i3)

Where:

- `N`: is an integer known at compile time that indicates the number of parallel cables.
- each complex number is represented by two real signals as (real,imag)

### `(si.)cmul`

Multiply two complex signals pointwise. `cmul` is a standard Faust function.

#### Usage

    (r1,i1) : cmul(r2,i2) : (_,_)

Where:

- Each complex number is represented by two real signals as (real,imag), so
- `(r1,i1)` = real and imaginary parts of signal 1
- `(r2,i2)` = real and imaginary parts of signal 2

### `(si.)cconj`

Complex conjugation of a (complex) signal. `cconj` is a standard Faust function.

#### Usage

    (r1,i1) : cconj : (_,_)

Where:

- Each complex number is represented by two real signals as (real,imag), so
- `(r1,i1)` = real and imaginary parts of the input signal
- `(r1,-i1)` = real and imaginary parts of the output signal

### `(si.)onePoleSwitching`

One pole filter with independent attack and release times.

#### Usage

    _ : onePoleSwitching(att,rel) : _

Where:

- `att`: the attack tau time constant in second
- `rel`: the release tau time constant in second

### `(si.)rev`

Reverse the input signal by blocks of n>0 samples. `rev(1)` is the indentity function. `rev(n)` has a latency of `n-1` samples.

#### Usage

    _ : rev(n) : _

Where:

- `n`: the block size in samples

### `(si.)vecOp`

This function is a generalisation of Faust's iterators such as `prod` and `sum`, and it allows to perform operations on an arbitrary number of vectors, provided that they all have the same length. Unlike Faust's iterators `prod` and `sum` where the vector size is equal to one and the vector space dimension must be specified by the user, this function will infer the vector space dimension and vector size based on the vectors list that we provide.

The outputs of the function are equal to the vector size, whereas the number of inputs is dependent on whether the elements of the vectors provided expect an incoming signal themselves or not. We will see a clarifying example later; in general, the number of total inputs will be the sum of the inputs in each input vector.

Note that we must provide a list of at least two vectors, each with a size that is greater or equal to one.

#### Usage

         si.bus(inputs(vectorsList)) : vecOp((vectorsList), op) : si.bus(outputs(ba.take(1, vectorsList)));

#### Where

- `vectorsList`: is a list of vectors
- `op`: is a two-input, one-output operator

For example, consider the following vectors lists:

     v0 = (0 , 1 , 2 , 3);
     v1 = (4 , 5 , 6 , 7);
     v2 = (8 , 9 , 10 , 11);
     v3 = (12 , 13 , 14 , 15);
     v4 = (+(16) , _ , 18 , *(19));
     vv = (v0 , v1 , v2 , v3);

Although Faust has limitations for list processing, these vectors can be combined or processed individually.

If we do:

     process = vecOp(v0, +);

the function will deduce a vector space of dimension equal to four and a vector length equal to one. Note that this is equivalent to writing:

     process = v0 : sum(i, 4, _);

Similarly, we can write:

     process = vecOp((v0 , v1), *) :> _;

and we have a dimension-two space and length-four vectors. This is the dot product between vectors v0 and v1, which is equivalent to writing:

     process = v0 , v1 : dot(4);

The examples above have no inputs, as none of the elements of the vectors expect inputs. On the other hand, we can write:

     process = vecOp((v4 , v4), +);

and the function will have six inputs and four outputs, as each vector has three of the four elements expecting an input, times two, as the two input vectors are identical.

Finally, we can write:

     process = vecOp(vv, &);

to perform the bitwise AND on all the elements at the same position in each vector, having dimension equal to the vector length equal to four.

Or even:

     process = vecOp((vv , vv), &);

which gives us a dimension equal to two, and a vector size equal to sixteen.

For a more practical use-case, this is how we can implement a time-invariant feedback delay network with Hadamard matrix:

     N = 4;
     normalisation = 1.0 / sqrt(N);
     coeffVec = par(i, N, .99 * normalisation);
     delVec = par(i, N, (i + 1) * 3);
     process = vecOp((si.bus(N) , si.bus(N)), +) ~
         vecOp((vecOp((ro.hadamard(N) , coeffVec), *) , delVec), @);

### `(si.)bpar`

Balanced `par` where the repeated expression doesn't depend on a variable. The built-in `par` is implemented as an unbalanced tree, and also has to substitute the variable into the repeated expression, which is expensive even when the variable doesn't appear. This version is implemented as a balanced tree (which allows node reuse during tree traversal) and also doesn't search for the variable. This can be much faster than `par` to compile.

#### Usage

    si.bus(N * inputs(f)) : bpar(N, f) : si.bus(N * outputs(f))

Where:

- `N`: number of repetitions, minimum 1, a constant numerical expression
- `f`: an arbitrary expression

Example:

    // square each of 4000 inputs
    process = si.bpar(4000, (_ <: _, _ : *));

### `(si.)bsum`

Balanced `sum`, see `si.bpar`.

#### Usage

    si.bus(N * inputs(f)) : bsum(N, f) : _

Where:

- `N`: number of repetitions, minimum 1, a constant numerical expression
- `f`: an arbitrary expression with 1 output.

Example:

    // square each of 1000 inputs and add the results
    process = si.bsum(1000, (_ <: _, _ : *));

### `(si.)bprod`

Balanced `prod`, see `si.bpar`.

#### Usage

    si.bus(N * inputs(f)) : bprod(N, f) : _

Where:

- `N`: number of repetitions, minimum 1, a constant numerical expression
- `f`: an arbitrary expression with 1 output.

Example:

    // Add 8000 consecutive inputs (in pairs) and multiply the results
    process = si.bprod(4000, +);

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