Digital signal processing routines and classes. More...

Classes
struct	AppleRingBuffer
	A cyclic buffer which maintains a valid linear array of size S by sliding along a larger block of size N. More...

struct	BooleanTrigger
	Detects when a boolean changes from false to true. More...

struct	ClockDivider
	Counts calls to process(), returning true every `division` calls. More...

struct	ComplexFFT
	Complex-valued FFT context. More...

struct	Decimator
	Downsamples by an integer factor. More...

struct	DoubleRingBuffer
	A cyclic buffer which maintains a valid linear array of size S by keeping a copy of the buffer in adjacent memory. More...

struct	Frame
	Useful for storing arrays of samples in ring buffers and casting them to `float*` to be used by interleaved processors, like SampleRateConverter. More...

struct	IIRFilter
	Digital IIR filter processor. More...

struct	MidiGenerator
	Converts gates and CV to MIDI messages. More...

struct	MidiParser
	Converts MIDI note and transport messages to gates, CV, and other states. More...

struct	MinBlepGenerator

struct	PulseGenerator
	When triggered, holds a high value for a specified time before going low again. More...

struct	RealFFT
	Real-valued FFT context. More...

struct	RealTimeConvolver

struct	RingBuffer
	Lock-free queue with fixed size and no allocations. More...

struct	SampleRateConverter
	Resamples by a fixed rational factor. More...

struct	TBiquadFilter

struct	TExponentialFilter
	Applies exponential smoothing to a signal with the ODE \( \frac{dy}{dt} = x \lambda \). More...

struct	TExponentialSlewLimiter
	Behaves like ExponentialFilter but with different lambas when the RHS of the ODE is positive or negative. More...

struct	TPeakFilter
	Like ExponentialFilter but jumps immediately to higher values. More...

struct	TRCFilter
	The simplest possible analog filter using an Euler solver. More...

struct	TSchmittTrigger
	Turns HIGH when value reaches a threshold (default 0.f), turns LOW when value reaches a threshold (default 1.f). More...

struct	TSchmittTrigger< float >

struct	TSlewLimiter
	Limits the derivative of the output by a rise and fall speed, in units/s. More...

struct	TTimer
	Accumulates a timer when process() is called. More...

struct	Upsampler
	Upsamples by an integer factor. More...

struct	VuMeter
	Deprecated. More...

struct	VuMeter2
	Models a VU meter with smoothing. More...

Typedefs
typedef TSchmittTrigger	SchmittTrigger

typedef TTimer	Timer

typedef TRCFilter	RCFilter

typedef TExponentialFilter	ExponentialFilter

typedef TPeakFilter	PeakFilter

typedef TSlewLimiter	SlewLimiter

typedef TExponentialSlewLimiter	ExponentialSlewLimiter

typedef TBiquadFilter	BiquadFilter

Functions
template<typename T , size_t N>
T	polyDirect (const T(&a)[N], T x)
	Evaluates a polynomial with coefficients `a[n]` at `x`.

template<typename T , size_t N>
T	polyHorner (const T(&a)[N], T x)
	Evaluates a polynomial with coefficients `a[n]` at `x`.

template<typename T , size_t N>
T	polyEstrin (const T(&a)[N], T x)
	Evaluates a polynomial with coefficients `a[n]` at `x`.

template<typename T >
T	exp2Floor (T x, T *xf)
	Returns `2^floor(x)`.

template<>
float	exp2Floor (float x, float *xf)

template<>
simd::float_4	exp2Floor (simd::float_4 x, simd::float_4 *xf)

template<typename T >
T	approxExp2Floor (T x, T *xf)
	Deprecated alias of exp2Floor()

template<typename T >
T	exp2_taylor5 (T x)
	Returns 2^x with at most 6e-06 relative error.

template<typename T >
T	approxExp2_taylor5 (T x)
	Deprecated alias of exp2_taylor5()

float	sinc (float x)
	The normalized sinc function See https://en.wikipedia.org/wiki/Sinc_function.

template<typename T >
T	sinc (T x)

template<typename T >
T	amplitudeToDb (T amp)

template<typename T >
T	dbToAmplitude (T db)

template<typename T >
T	quadraticBipolar (T x)

template<typename T >
T	cubic (T x)

template<typename T >
T	quarticBipolar (T x)

template<typename T >
T	quintic (T x)

template<typename T >
T	sqrtBipolar (T x)

template<typename T >
T	exponentialBipolar (T b, T x)
	This is pretty much a scaled sinh.

struct	__attribute__ ((packed, aligned(1), gcc_struct)) Int24
	24-bit integer, using int32_t for conversions.

template<typename To , typename From >
To	convert (From x)=delete
	Converts between normalized types.

template<>
float	convert (float x)
	Trivial conversions.

template<>
float	convert (int8_t x)
	Integer to float.

template<>
float	convert (int16_t x)

template<>
float	convert (Int24 x)

template<>
float	convert (int32_t x)

template<>
float	convert (int64_t x)

template<>
int8_t	convert (float x)
	Float to integer.

template<>
int16_t	convert (float x)

template<>
Int24	convert (float x)

template<>
int32_t	convert (float x)

template<>
int64_t	convert (float x)

template<typename To , typename From >
void	convert (const From in, To out, size_t len)
	Buffer conversion.

float	convolveNaive (const float in, const float kernel, int len)
	Performs a direct sum convolution.

void	boxcarLowpassIR (float *out, int len, float cutoff=0.5f)
	Computes the impulse response of a boxcar lowpass filter.

void	minBlepImpulse (int z, int o, float *output)
	Computes the minimum-phase bandlimited step (MinBLEP) z: number of zero-crossings o: oversample factor output: must be length `2 * z * o`.

template<typename T , typename F >
void	stepEuler (T t, T dt, T x[], int len, F f)
	The callback function `f` in each of these stepping functions must have the signature.

template<typename T , typename F >
void	stepRK2 (T t, T dt, T x[], int len, F f)
	Solves an ODE system using the 2nd order Runge-Kutta method.

template<typename T , typename F >
void	stepRK4 (T t, T dt, T x[], int len, F f)
	Solves an ODE system using the 4th order Runge-Kutta method.

template<typename T >
T	hann (T p)
	Hann window function.

void	hannWindow (float *x, int len)
	Multiplies the Hann window by a signal `x` of length `len` in-place.

template<typename T >
T	blackman (T alpha, T p)
	Blackman window function.

void	blackmanWindow (float alpha, float *x, int len)

template<typename T >
T	blackmanNuttall (T p)
	Blackman-Nuttall window function.

void	blackmanNuttallWindow (float *x, int len)

template<typename T >
T	blackmanHarris (T p)
	Blackman-Harris window function.

void	blackmanHarrisWindow (float *x, int len)

Variables
DEPRECATED typedef VuMeter	VUMeter

static const float	FREQ_C4 = 261.6256f

static const float	FREQ_A4 = 440.0000f

static const float	FREQ_SEMITONE = 1.0594630943592953f

Detailed Description

Digital signal processing routines and classes.

Typedef Documentation

◆ SchmittTrigger

typedef TSchmittTrigger rack::dsp::SchmittTrigger

◆ Timer

typedef TTimer rack::dsp::Timer

◆ RCFilter

typedef TRCFilter rack::dsp::RCFilter

◆ ExponentialFilter

typedef TExponentialFilter rack::dsp::ExponentialFilter

◆ PeakFilter

typedef TPeakFilter rack::dsp::PeakFilter

◆ SlewLimiter

typedef TSlewLimiter rack::dsp::SlewLimiter

◆ ExponentialSlewLimiter

typedef TExponentialSlewLimiter rack::dsp::ExponentialSlewLimiter

◆ BiquadFilter

typedef TBiquadFilter rack::dsp::BiquadFilter

Function Documentation

◆ polyDirect()

template<typename T , size_t N>

T rack::dsp::polyDirect	(	const T(&)	a[N],
		T	x )

Evaluates a polynomial with coefficients a[n] at x.

Uses naive direct evaluation.

◆ polyHorner()

template<typename T , size_t N>

T rack::dsp::polyHorner	(	const T(&)	a[N],
		T	x )

Evaluates a polynomial with coefficients a[n] at x.

Uses Horner's method. https://en.wikipedia.org/wiki/Horner%27s_method

◆ polyEstrin()

template<typename T , size_t N>

T rack::dsp::polyEstrin	(	const T(&)	a[N],
		T	x )

Evaluates a polynomial with coefficients a[n] at x.

Uses Estrin's method. https://en.wikipedia.org/wiki/Estrin%27s_scheme

◆ exp2Floor() [1/3]

template<typename T >

T rack::dsp::exp2Floor	(	T	x,
		T *	xf )

Returns 2^floor(x).

If xf is given, sets it to the fractional part of x. This is useful in the computation 2^x = 2^floor(x) * 2^frac(x).

◆ exp2Floor() [2/3]

template<>

float rack::dsp::exp2Floor	(	float	x,
		float *	xf )

inline

◆ exp2Floor() [3/3]

template<>

simd::float_4 rack::dsp::exp2Floor	(	simd::float_4	x,
		simd::float_4 *	xf )

inline

◆ approxExp2Floor()

template<typename T >

T rack::dsp::approxExp2Floor	(	T	x,
		T *	xf )

Deprecated alias of exp2Floor()

◆ exp2_taylor5()

template<typename T >

T rack::dsp::exp2_taylor5 ( T x )

Returns 2^x with at most 6e-06 relative error.

Polynomial coefficients are chosen to minimize relative error while maintaining continuity and giving exact values at integer values of x. Thanks to Andy Simper for coefficients.

◆ approxExp2_taylor5()

template<typename T >

T rack::dsp::approxExp2_taylor5 ( T x )

Deprecated alias of exp2_taylor5()

◆ sinc() [1/2]

float rack::dsp::sinc ( float x )

inline

The normalized sinc function See https://en.wikipedia.org/wiki/Sinc_function.

◆ sinc() [2/2]

template<typename T >

T rack::dsp::sinc ( T x )

◆ amplitudeToDb()

template<typename T >

T rack::dsp::amplitudeToDb ( T amp )

◆ dbToAmplitude()

template<typename T >

T rack::dsp::dbToAmplitude ( T db )

◆ quadraticBipolar()

template<typename T >

T rack::dsp::quadraticBipolar ( T x )

◆ cubic()

template<typename T >

T rack::dsp::cubic ( T x )

◆ quarticBipolar()

template<typename T >

T rack::dsp::quarticBipolar ( T x )

◆ quintic()

template<typename T >

T rack::dsp::quintic ( T x )

◆ sqrtBipolar()

template<typename T >

T rack::dsp::sqrtBipolar ( T x )

◆ exponentialBipolar()

template<typename T >

T rack::dsp::exponentialBipolar	(	T	b,
		T	x )

This is pretty much a scaled sinh.

Slow. Not recommended for parameter scaling.

◆ attribute()

struct rack::dsp::__attribute__ ( (packed, aligned(1), gcc_struct) )

24-bit integer, using int32_t for conversions.

◆ convert() [1/13]

template<typename To , typename From >

To rack::dsp::convert ( From x )

delete

Converts between normalized types.

◆ convert() [2/13]

template<>

float rack::dsp::convert ( float x )

inline

Trivial conversions.

◆ convert() [3/13]

template<>

float rack::dsp::convert ( int8_t x )

inline

Integer to float.

◆ convert() [4/13]

template<>

float rack::dsp::convert ( int16_t x )

inline

◆ convert() [5/13]

template<>

float rack::dsp::convert ( Int24 x )

inline

◆ convert() [6/13]

template<>

float rack::dsp::convert ( int32_t x )

inline

◆ convert() [7/13]

template<>

float rack::dsp::convert ( int64_t x )

inline

◆ convert() [8/13]

template<>

int8_t rack::dsp::convert ( float x )

inline

Float to integer.

◆ convert() [9/13]

template<>

int16_t rack::dsp::convert ( float x )

inline

◆ convert() [10/13]

template<>

Int24 rack::dsp::convert ( float x )

inline

◆ convert() [11/13]

template<>

int32_t rack::dsp::convert ( float x )

inline

◆ convert() [12/13]

template<>

int64_t rack::dsp::convert ( float x )

inline

◆ convert() [13/13]

template<typename To , typename From >

void rack::dsp::convert	(	const From *	in,
		To *	out,
		size_t	len )

Buffer conversion.

◆ convolveNaive()

float rack::dsp::convolveNaive	(	const float *	in,
		const float *	kernel,
		int	len )

inline

Performs a direct sum convolution.

◆ boxcarLowpassIR()

void rack::dsp::boxcarLowpassIR	(	float *	out,
		int	len,
		float	cutoff = 0.5f )

inline

Computes the impulse response of a boxcar lowpass filter.

◆ minBlepImpulse()

void rack::dsp::minBlepImpulse	(	int	z,
		int	o,
		float *	output )

Computes the minimum-phase bandlimited step (MinBLEP) z: number of zero-crossings o: oversample factor output: must be length 2 * z * o.

https://www.cs.cmu.edu/~eli/papers/icmc01-hardsync.pdf

◆ stepEuler()

template<typename T , typename F >

void rack::dsp::stepEuler	(	T	t,
		T	dt,
		T	x[],
		int	len,
		F	f )

The callback function f in each of these stepping functions must have the signature.

void f(T t, const T x[], T dxdt[])

A capturing lambda is ideal for this. For example, the following solves the system x''(t) = -x(t) using a fixed timestep of 0.01 and initial conditions x(0) = 1, x'(0) = 0.

float x[2] = {1.f, 0.f};
float dt = 0.01f;
for (float t = 0.f; t < 1.f; t += dt) {
    rack::ode::stepRK4(t, dt, x, 2, [&](float t, const float x[], float dxdt[]) {
        dxdt[0] = x[1];
        dxdt[1] = -x[0];
    });
    printf("%f\n", x[0]);
}

Solves an ODE system using the 1st order Euler method

◆ stepRK2()

template<typename T , typename F >

void rack::dsp::stepRK2	(	T	t,
		T	dt,
		T	x[],
		int	len,
		F	f )

Solves an ODE system using the 2nd order Runge-Kutta method.

◆ stepRK4()

template<typename T , typename F >

void rack::dsp::stepRK4	(	T	t,
		T	dt,
		T	x[],
		int	len,
		F	f )

Solves an ODE system using the 4th order Runge-Kutta method.

◆ hann()

template<typename T >

T rack::dsp::hann ( T p )

inline

Hann window function.

p: proportion from [0, 1], usually i / (len - 1) https://en.wikipedia.org/wiki/Window_function#Hann_and_Hamming_windows

◆ hannWindow()

void rack::dsp::hannWindow	(	float *	x,
		int	len )

inline

Multiplies the Hann window by a signal x of length len in-place.

◆ blackman()

template<typename T >

T rack::dsp::blackman	(	T	alpha,
		T	p )

inline

Blackman window function.

https://en.wikipedia.org/wiki/Window_function#Blackman_window A typical alpha value is 0.16.

◆ blackmanWindow()

void rack::dsp::blackmanWindow	(	float	alpha,
		float *	x,
		int	len )

inline

◆ blackmanNuttall()

template<typename T >

T rack::dsp::blackmanNuttall ( T p )

inline

Blackman-Nuttall window function.

https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Nuttall_window

◆ blackmanNuttallWindow()

void rack::dsp::blackmanNuttallWindow	(	float *	x,
		int	len )

inline

◆ blackmanHarris()

template<typename T >

T rack::dsp::blackmanHarris ( T p )

inline

Blackman-Harris window function.

https://en.wikipedia.org/wiki/Window_function#Blackman%E2%80%93Harris_window

◆ blackmanHarrisWindow()

void rack::dsp::blackmanHarrisWindow	(	float *	x,
		int	len )

inline

Variable Documentation

◆ VUMeter

DEPRECATED typedef VuMeter rack::dsp::VUMeter

◆ FREQ_C4

const float rack::dsp::FREQ_C4 = 261.6256f

static

◆ FREQ_A4

const float rack::dsp::FREQ_A4 = 440.0000f

static

◆ FREQ_SEMITONE

const float rack::dsp::FREQ_SEMITONE = 1.0594630943592953f

static

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ SchmittTrigger

◆ Timer

◆ RCFilter

◆ ExponentialFilter

◆ PeakFilter

◆ SlewLimiter

◆ ExponentialSlewLimiter

◆ BiquadFilter

Function Documentation

◆ polyDirect()

◆ polyHorner()

◆ polyEstrin()

◆ exp2Floor() [1/3]

◆ exp2Floor() [2/3]

◆ exp2Floor() [3/3]

◆ approxExp2Floor()

◆ exp2_taylor5()

◆ approxExp2_taylor5()

◆ sinc() [1/2]

◆ sinc() [2/2]

◆ amplitudeToDb()

◆ dbToAmplitude()

◆ quadraticBipolar()

◆ cubic()

◆ quarticBipolar()

◆ quintic()

◆ sqrtBipolar()

◆ exponentialBipolar()

◆ __attribute__()

◆ convert() [1/13]

◆ convert() [2/13]

◆ convert() [3/13]

◆ convert() [4/13]

◆ convert() [5/13]

◆ convert() [6/13]

◆ convert() [7/13]

◆ convert() [8/13]

◆ convert() [9/13]

◆ convert() [10/13]

◆ convert() [11/13]

◆ convert() [12/13]

◆ convert() [13/13]

◆ convolveNaive()

◆ boxcarLowpassIR()

◆ minBlepImpulse()

◆ stepEuler()

◆ stepRK2()

◆ stepRK4()

◆ hann()

◆ hannWindow()

◆ blackman()

◆ blackmanWindow()

◆ blackmanNuttall()

◆ blackmanNuttallWindow()

◆ blackmanHarris()

◆ blackmanHarrisWindow()

Variable Documentation

◆ VUMeter

◆ FREQ_C4

◆ FREQ_A4

◆ FREQ_SEMITONE

◆ attribute()