Digital signal processing routines. 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

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	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
	A simple cyclic buffer. 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

struct	Timer

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 1.f, turns LOW when value reaches 0.f. More...

struct	TSchmittTrigger< float >

struct	TSlewLimiter

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 TRCFilter	RCFilter

typedef TExponentialFilter	ExponentialFilter

typedef TPeakFilter	PeakFilter

typedef TSlewLimiter	SlewLimiter

typedef TExponentialSlewLimiter	ExponentialSlewLimiter

typedef TBiquadFilter	BiquadFilter

Functions
template<typename T >
T	approxExp2Floor (T x, T *xf)
	Returns 2^floor(x), assuming that x >= 0. More...

template<>
simd::float_4	approxExp2Floor (simd::float_4 x, simd::float_4 *xf)

template<>
float	approxExp2Floor (float x, float *xf)

template<typename T >
T	approxExp2_taylor5 (T x)
	Returns 2^x, assuming that x >= 0. More...

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

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. More...

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

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

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`. More...

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. More...

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. More...

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. More...

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

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

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

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

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

void	blackmanNuttallWindow (float *x, int len)

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

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.

Typedef Documentation

◆ SchmittTrigger

typedef TSchmittTrigger rack::dsp::SchmittTrigger

◆ 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

◆ approxExp2Floor() [1/3]

template<typename T >

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

Returns 2^floor(x), assuming that x >= 0.

If xf is non-NULL, it is set to the fractional part of x.

◆ approxExp2Floor() [2/3]

template<>

simd::float_4 rack::dsp::approxExp2Floor	(	simd::float_4	x,
		simd::float_4 *	xf
	)

inline

◆ approxExp2Floor() [3/3]

template<>

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

inline

◆ approxExp2_taylor5()

template<typename T >

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

Returns 2^x, assuming that x >= 0.

Maximum 0.00024% error. For float, roughly 3x faster than std::pow(2.f, x). For float_4, roughly 2x faster than simd::pow(2.f, x).

If negative powers are needed, you may use a lower bound and rescale.

approxExp2(x + 20) / 1048576

◆ 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.

◆ 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

◆ RCFilter

◆ ExponentialFilter

◆ PeakFilter

◆ SlewLimiter

◆ ExponentialSlewLimiter

◆ BiquadFilter

Function Documentation

◆ approxExp2Floor() [1/3]

◆ approxExp2Floor() [2/3]

◆ approxExp2Floor() [3/3]

◆ approxExp2_taylor5()

◆ sinc() [1/2]

◆ sinc() [2/2]

◆ amplitudeToDb()

◆ dbToAmplitude()

◆ quadraticBipolar()

◆ cubic()

◆ quarticBipolar()

◆ quintic()

◆ sqrtBipolar()

◆ exponentialBipolar()

◆ convolveNaive()

◆ boxcarLowpassIR()

◆ minBlepImpulse()

◆ stepEuler()

◆ stepRK2()

◆ stepRK4()

◆ hann()

◆ hannWindow()

◆ blackman()

◆ blackmanWindow()

◆ blackmanNuttall()

◆ blackmanNuttallWindow()

◆ blackmanHarris()

◆ blackmanHarrisWindow()

Variable Documentation

◆ VUMeter

◆ FREQ_C4

◆ FREQ_A4

◆ FREQ_SEMITONE