perform Discrete Fourier Transforms More...

#include <vtkFFT.h>

Inheritance diagram for vtkFFT:

Collaboration diagram for vtkFFT:

Classes
struct	isFftType

struct	isFftType< vtkFFT::ComplexNumber >

struct	isFftType< vtkFFT::ScalarNumber >

Public Types
enum	Octave { Hz_31_5 = 5 , Hz_63 = 6 , Hz_125 = 7 , Hz_250 = 8 , Hz_500 = 9 , kHz_1 = 10 , kHz_2 = 11 , kHz_4 = 12 , kHz_8 = 13 , kHz_16 = 14 }
	Enum containing octave band numbers, named upon their nominal midband frequency. More...

enum	OctaveSubdivision { Full , FirstHalf , SecondHalf , FirstThird , SecondThird , ThirdThird }
	Enum specifying which octave band we want to compute. More...

enum	Scaling : int { Density = 0 , Spectrum }
	Scaling modes for Spectrogram and Csd functions. More...

enum	SpectralMode : int { STFT = 0 , PSD }
	Spectral modes for Spectrogram and Csd functions. More...

typedef vtkObject	Superclass


using	ScalarNumber = kiss_fft_scalar
	Useful type definitions and utilities.

using	ComplexNumber = kiss_fft_cpx
	Useful type definitions and utilities.

using	vtkScalarNumberArray = vtkAOSDataArrayTemplate< vtkFFT::ScalarNumber >
	Useful type definitions and utilities.

Public Member Functions
virtual vtkTypeBool	IsA (const char *type)
	Return 1 if this class is the same type of (or a subclass of) the named class.

vtkFFT *	NewInstance () const

void	PrintSelf (ostream &os, vtkIndent indent) override
	Methods invoked by print to print information about the object including superclasses.

template<>
constexpr vtkFFT::ComplexNumber	Zero ()

Public Member Functions inherited from vtkObject
	vtkBaseTypeMacro (vtkObject, vtkObjectBase)

virtual void	DebugOn ()
	Turn debugging output on.

virtual void	DebugOff ()
	Turn debugging output off.

bool	GetDebug ()
	Get the value of the debug flag.

void	SetDebug (bool debugFlag)
	Set the value of the debug flag.

virtual void	Modified ()
	Update the modification time for this object.

virtual vtkMTimeType	GetMTime ()
	Return this object's modified time.

void	PrintSelf (ostream &os, vtkIndent indent) override
	Methods invoked by print to print information about the object including superclasses.

void	RemoveObserver (unsigned long tag)

void	RemoveObservers (unsigned long event)

void	RemoveObservers (const char *event)

void	RemoveAllObservers ()

vtkTypeBool	HasObserver (unsigned long event)

vtkTypeBool	HasObserver (const char *event)

vtkTypeBool	InvokeEvent (unsigned long event)

vtkTypeBool	InvokeEvent (const char *event)

std::string	GetObjectDescription () const override
	The object description printed in messages and PrintSelf output.

unsigned long	AddObserver (unsigned long event, vtkCommand *, float priority=0.0f)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

unsigned long	AddObserver (const char event, vtkCommand , float priority=0.0f)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

vtkCommand *	GetCommand (unsigned long tag)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

void	RemoveObserver (vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

void	RemoveObservers (unsigned long event, vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

void	RemoveObservers (const char event, vtkCommand )
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

vtkTypeBool	HasObserver (unsigned long event, vtkCommand *)
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

vtkTypeBool	HasObserver (const char event, vtkCommand )
	Allow people to add/remove/invoke observers (callbacks) to any VTK object.

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::*callback)(), float priority=0.0f)
	Overloads to AddObserver that allow developers to add class member functions as callbacks for events.

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, void(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)
	Overloads to AddObserver that allow developers to add class member functions as callbacks for events.

template<class U , class T >
unsigned long	AddObserver (unsigned long event, U observer, bool(T::callback)(vtkObject , unsigned long, void *), float priority=0.0f)
	Allow user to set the AbortFlagOn() with the return value of the callback method.

vtkTypeBool	InvokeEvent (unsigned long event, void *callData)
	This method invokes an event and return whether the event was aborted or not.

vtkTypeBool	InvokeEvent (const char event, void callData)
	This method invokes an event and return whether the event was aborted or not.

virtual void	SetObjectName (const std::string &objectName)
	Set/get the name of this object for reporting purposes.

virtual std::string	GetObjectName () const
	Set/get the name of this object for reporting purposes.

Public Member Functions inherited from vtkObjectBase
const char *	GetClassName () const
	Return the class name as a string.

virtual std::string	GetObjectDescription () const
	The object description printed in messages and PrintSelf output.

virtual vtkTypeBool	IsA (const char *name)
	Return 1 if this class is the same type of (or a subclass of) the named class.

virtual vtkIdType	GetNumberOfGenerationsFromBase (const char *name)
	Given the name of a base class of this class type, return the distance of inheritance between this class type and the named class (how many generations of inheritance are there between this class and the named class).

virtual void	Delete ()
	Delete a VTK object.

virtual void	FastDelete ()
	Delete a reference to this object.

void	InitializeObjectBase ()

void	Print (ostream &os)
	Print an object to an ostream.

void	Register (vtkObjectBase *o)
	Increase the reference count (mark as used by another object).

virtual void	UnRegister (vtkObjectBase *o)
	Decrease the reference count (release by another object).

int	GetReferenceCount ()
	Return the current reference count of this object.

void	SetReferenceCount (int)
	Sets the reference count.

bool	GetIsInMemkind () const
	A local state flag that remembers whether this object lives in the normal or extended memory space.

virtual void	PrintHeader (ostream &os, vtkIndent indent)
	Methods invoked by print to print information about the object including superclasses.

virtual void	PrintTrailer (ostream &os, vtkIndent indent)
	Methods invoked by print to print information about the object including superclasses.

virtual bool	UsesGarbageCollector () const
	Indicate whether the class uses `vtkGarbageCollector` or not.

Static Public Member Functions
static std::vector< ComplexNumber >	IFft (const std::vector< ComplexNumber > &in)
	Compute the inverse of `Fft`.

static std::vector< ScalarNumber >	IRFft (const std::vector< ComplexNumber > &in)
	Compute the inverse of `RFft`.

static ScalarNumber	Abs (const ComplexNumber &in)
	Return the absolute value (also known as norm, modulus, or magnitude) of complex number.

static ScalarNumber	SquaredAbs (const ComplexNumber &in)
	Return the squared absolute value of the complex number.

static ComplexNumber	Conjugate (const ComplexNumber &in)
	Return the conjugate of the given complex number.

static std::vector< ScalarNumber >	FftFreq (int windowLength, double sampleSpacing)
	Return the DFT sample frequencies.

static std::vector< ScalarNumber >	RFftFreq (int windowLength, double sampleSpacing)
	Return the DFT sample frequencies for the real version of the dft (see `Rfft`).

static std::array< double, 2 >	GetOctaveFrequencyRange (Octave octave, OctaveSubdivision octaveSubdivision=OctaveSubdivision::Full, bool baseTwo=true)
	Return lower and upper frequency from a octave band number / nominal midband frequency.

template<typename T >
static void	Transpose (T data, unsigned int shape)
	Transpose in place an inlined 2D matrix.

template<typename T >
static void	GenerateKernel1D (T *kernel, std::size_t n, WindowGenerator generator)
	Given a window generator function, create a symmetric 1D kernel.

template<typename T >
static void	GenerateKernel2D (T *kernel, std::size_t n, std::size_t m, WindowGenerator generator)
	Given a window generator function, create a symmetric 2D kernel.

static vtkFFT *	New ()

static vtkTypeBool	IsTypeOf (const char *type)

static vtkFFT *	SafeDownCast (vtkObjectBase *o)


static std::vector< ComplexNumber >	Fft (const std::vector< ScalarNumber > &in)
	Compute the one-dimensional DFT for complex input.

static void	Fft (ScalarNumber input, std::size_t size, ComplexNumber result)
	Compute the one-dimensional DFT for complex input.

static std::vector< ComplexNumber >	Fft (const std::vector< ComplexNumber > &in)
	Compute the one-dimensional DFT for complex input.

static void	Fft (ComplexNumber input, std::size_t size, ComplexNumber result)
	Compute the one-dimensional DFT for complex input.

static vtkSmartPointer< vtkScalarNumberArray >	Fft (vtkScalarNumberArray *input)
	Compute the one-dimensional DFT for complex input.


static std::vector< ComplexNumber >	RFft (const std::vector< ScalarNumber > &in)
	Compute the one-dimensional DFT for real input.

static void	RFft (ScalarNumber input, std::size_t size, ComplexNumber result)
	Compute the one-dimensional DFT for real input.

static vtkSmartPointer< vtkScalarNumberArray >	RFft (vtkScalarNumberArray *input)
	Compute the one-dimensional DFT for real input.


template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>
static std::vector< ComplexNumber >	OverlappingFft (const std::vector< T > &signal, const std::vector< TW > &window, std::size_t noverlap, bool detrend, bool onesided, unsigned int *shape=nullptr)
	Compute consecutive Fourier transforms Welch method without averaging nor scaling the result.

template<typename TW >
static vtkFFT::ComplexNumber *	OverlappingFft (vtkFFT::vtkScalarNumberArray signal, const std::vector< TW > &window, std::size_t noverlap, bool detrend, bool onesided, unsigned int shape=nullptr)
	Compute consecutive Fourier transforms Welch method without averaging nor scaling the result.


template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>
static std::vector< ComplexNumber >	Spectrogram (const std::vector< T > &signal, const std::vector< TW > &window, double sampleRate, int noverlap, bool detrend, bool onesided, vtkFFT::Scaling scaling, vtkFFT::SpectralMode mode, unsigned int *shape=nullptr, bool transpose=false)
	Compute a spectrogram with consecutive Fourier transforms using Welch method.

template<typename TW >
static vtkSmartPointer< vtkFFT::vtkScalarNumberArray >	Spectrogram (vtkFFT::vtkScalarNumberArray signal, const std::vector< TW > &window, double sampleRate, int noverlap, bool detrend, bool onesided, vtkFFT::Scaling scaling, vtkFFT::SpectralMode mode, unsigned int shape=nullptr, bool transpose=false)
	Compute a spectrogram with consecutive Fourier transforms using Welch method.


template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>
static std::vector< vtkFFT::ScalarNumber >	Csd (const std::vector< T > &signal, const std::vector< TW > &window, double sampleRate, int noverlap, bool detrend, bool onesided, vtkFFT::Scaling scaling)
	Compute the Cross Spectral Density of a given signal.

template<typename TW >
static vtkSmartPointer< vtkFFT::vtkScalarNumberArray >	Csd (vtkScalarNumberArray *signal, const std::vector< TW > &window, double sampleRate, int noverlap, bool detrend, bool onesided, vtkFFT::Scaling scaling)
	Compute the Cross Spectral Density of a given signal.

Static Public Member Functions inherited from vtkObject
static vtkObject *	New ()
	Create an object with Debug turned off, modified time initialized to zero, and reference counting on.

static void	BreakOnError ()
	This method is called when vtkErrorMacro executes.

static void	SetGlobalWarningDisplay (vtkTypeBool val)
	This is a global flag that controls whether any debug, warning or error messages are displayed.

static void	GlobalWarningDisplayOn ()
	This is a global flag that controls whether any debug, warning or error messages are displayed.

static void	GlobalWarningDisplayOff ()
	This is a global flag that controls whether any debug, warning or error messages are displayed.

static vtkTypeBool	GetGlobalWarningDisplay ()
	This is a global flag that controls whether any debug, warning or error messages are displayed.

Static Public Member Functions inherited from vtkObjectBase
static vtkTypeBool	IsTypeOf (const char *name)
	Return 1 if this class type is the same type of (or a subclass of) the named class.

static vtkIdType	GetNumberOfGenerationsFromBaseType (const char *name)
	Given a the name of a base class of this class type, return the distance of inheritance between this class type and the named class (how many generations of inheritance are there between this class and the named class).

static vtkObjectBase *	New ()
	Create an object with Debug turned off, modified time initialized to zero, and reference counting on.

static void	SetMemkindDirectory (const char *directoryname)
	The name of a directory, ideally mounted -o dax, to memory map an extended memory space within.

static bool	GetUsingMemkind ()
	A global state flag that controls whether vtkObjects are constructed in the usual way (the default) or within the extended memory space.

Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const

	vtkFFT ()=default

	~vtkFFT () override=default

Protected Member Functions inherited from vtkObject
	vtkObject ()

	~vtkObject () override

void	RegisterInternal (vtkObjectBase *, vtkTypeBool check) override

void	UnRegisterInternal (vtkObjectBase *, vtkTypeBool check) override

void	InternalGrabFocus (vtkCommand mouseEvents, vtkCommand keypressEvents=nullptr)
	These methods allow a command to exclusively grab all events.

void	InternalReleaseFocus ()
	These methods allow a command to exclusively grab all events.

Protected Member Functions inherited from vtkObjectBase
	vtkObjectBase ()

virtual	~vtkObjectBase ()

virtual void	RegisterInternal (vtkObjectBase *, vtkTypeBool check)

virtual void	UnRegisterInternal (vtkObjectBase *, vtkTypeBool check)

virtual void	ReportReferences (vtkGarbageCollector *)

virtual void	ObjectFinalize ()

	vtkObjectBase (const vtkObjectBase &)

void	operator= (const vtkObjectBase &)

Static Protected Member Functions
template<typename T >
static constexpr T	Zero ()
	Templated zero value, specialized for vtkFFT::ComplexNumber.

template<typename InputIt >
static std::iterator_traits< InputIt >::value_type	ComputeScaling (InputIt begin, InputIt end, Scaling scaling, double fs)
	For a given window defined by `begin` and `end`, compute the scaling needed to apply to the resulting FFT.

template<typename T , typename TW >
static void	PreprocessAndDispatchFft (const T segment, const std::vector< TW > &window, bool detrend, bool onesided, vtkFFT::ComplexNumber result)
	Dispatch the signal to the right FFT function according to the given parameters.

static void	RFft (ComplexNumber input, std::size_t size, ComplexNumber result)
	XXX(c++17): This function should NOT exist and is here just for the sake template unfolding purposes.

template<typename TW >
static void	ScaleFft (ComplexNumber *fft, unsigned int shape[2], const std::vector< TW > &window, double sampleRate, bool onesided, vtkFFT::Scaling scaling, vtkFFT::SpectralMode mode)
	Scale a fft according to its window and some mode.

Static Protected Member Functions inherited from vtkObjectBase
static vtkMallocingFunction	GetCurrentMallocFunction ()

static vtkReallocingFunction	GetCurrentReallocFunction ()

static vtkFreeingFunction	GetCurrentFreeFunction ()

static vtkFreeingFunction	GetAlternateFreeFunction ()

using	WindowGenerator = ScalarNumber(*)(std::size_t, std::size_t)
	Window generator functions.

static ScalarNumber	HanningGenerator (std::size_t x, std::size_t size)
	Window generator functions.

static ScalarNumber	BartlettGenerator (std::size_t x, std::size_t size)
	Window generator functions.

static ScalarNumber	SineGenerator (std::size_t x, std::size_t size)
	Window generator functions.

static ScalarNumber	BlackmanGenerator (std::size_t x, std::size_t size)
	Window generator functions.

static ScalarNumber	RectangularGenerator (std::size_t x, std::size_t size)
	Window generator functions.

Additional Inherited Members
Protected Attributes inherited from vtkObject
bool	Debug

vtkTimeStamp	MTime

vtkSubjectHelper *	SubjectHelper

std::string	ObjectName

Protected Attributes inherited from vtkObjectBase
std::atomic< int32_t >	ReferenceCount

vtkWeakPointerBase **	WeakPointers

Detailed Description

perform Discrete Fourier Transforms

vtkFFT provides methods to perform Discrete Fourier Transforms (DFT). These include providing forward and reverse Fourier transforms. The current implementation uses the third-party library kissfft.

The terminology tries to follow the Numpy terminology, that is :

Fft means the Fast Fourier Transform algorithm
Prefix R stands for Real (meaning optimized function for real inputs)
Prefix I stands for Inverse

Some functions provides pointer-based version of themself in order to prevent copying memory when possible.

Tests:: vtkFFT (Tests)

Definition at line 47 of file vtkFFT.h.

Member Typedef Documentation

◆ ScalarNumber

using vtkFFT::ScalarNumber = kiss_fft_scalar

Useful type definitions and utilities.

ScalarNumber is defined as a floating point number.

ComplexNumber is defined as a struct that contains two ScalarNumber. These 2 numbers should be contiguous in memory. First one should be named r and represent the real part, while second one should be named i and represent the imaginary part. This specification is important for the implementation of functions accepting and returning values from vtkDataArrays as it allows to do some zero-copy operations.

A vtkScalarNumberArray is a data array with a layout memory compatible with the underlying library for zero copy operations.

isFftType is a trait to tell templates if Type is either ScalarNumber or ComplexNumber.

Common operators such as +,-,*,/ between ScalarNumber and ComplexNumber are included in this header.

Definition at line 73 of file vtkFFT.h.

◆ ComplexNumber

using vtkFFT::ComplexNumber = kiss_fft_cpx

Useful type definitions and utilities.

ScalarNumber is defined as a floating point number.

ComplexNumber is defined as a struct that contains two ScalarNumber. These 2 numbers should be contiguous in memory. First one should be named r and represent the real part, while second one should be named i and represent the imaginary part. This specification is important for the implementation of functions accepting and returning values from vtkDataArrays as it allows to do some zero-copy operations.

A vtkScalarNumberArray is a data array with a layout memory compatible with the underlying library for zero copy operations.

isFftType is a trait to tell templates if Type is either ScalarNumber or ComplexNumber.

Common operators such as +,-,*,/ between ScalarNumber and ComplexNumber are included in this header.

Definition at line 74 of file vtkFFT.h.

◆ vtkScalarNumberArray

using vtkFFT::vtkScalarNumberArray = vtkAOSDataArrayTemplate<vtkFFT::ScalarNumber>

Useful type definitions and utilities.

ScalarNumber is defined as a floating point number.

ComplexNumber is defined as a struct that contains two ScalarNumber. These 2 numbers should be contiguous in memory. First one should be named r and represent the real part, while second one should be named i and represent the imaginary part. This specification is important for the implementation of functions accepting and returning values from vtkDataArrays as it allows to do some zero-copy operations.

A vtkScalarNumberArray is a data array with a layout memory compatible with the underlying library for zero copy operations.

isFftType is a trait to tell templates if Type is either ScalarNumber or ComplexNumber.

Common operators such as +,-,*,/ between ScalarNumber and ComplexNumber are included in this header.

Definition at line 78 of file vtkFFT.h.

◆ WindowGenerator

using vtkFFT::WindowGenerator = ScalarNumber (*)(std::size_t, std::size_t)

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 358 of file vtkFFT.h.

◆ Superclass

typedef vtkObject vtkFFT::Superclass

Definition at line 382 of file vtkFFT.h.

Member Enumeration Documentation

◆ Octave

enum vtkFFT::Octave

Enum containing octave band numbers, named upon their nominal midband frequency.

Value multiplied by 3 should be a one-third-octave band number matching an octave band.

Enumerator
Hz_31_5
Hz_63
Hz_125
Hz_250
Hz_500
kHz_1
kHz_2
kHz_4
kHz_8
kHz_16

Definition at line 89 of file vtkFFT.h.

◆ OctaveSubdivision

enum vtkFFT::OctaveSubdivision

Enum specifying which octave band we want to compute.

Could be a full octave range, or a one-third-octave one for instance.

Enumerator
Full
FirstHalf
SecondHalf
FirstThird
SecondThird
ThirdThird

Definition at line 107 of file vtkFFT.h.

◆ Scaling

enum vtkFFT::Scaling : int

Scaling modes for Spectrogram and Csd functions.

Enumerator
Density	Cross Spectral Density scaling (V^2/Hz)
Spectrum	Cross Spectrum scaling (V^2)

Definition at line 242 of file vtkFFT.h.

◆ SpectralMode

enum vtkFFT::SpectralMode : int

Spectral modes for Spectrogram and Csd functions.

Enumerator
STFT	Short-Time Fourier Transform, for local sections.
PSD	Power Spectral Density.

Definition at line 251 of file vtkFFT.h.

Constructor & Destructor Documentation

◆ vtkFFT()

vtkFFT::vtkFFT ( )

protecteddefault

◆ ~vtkFFT()

vtkFFT::~vtkFFT ( )

overrideprotecteddefault

Member Function Documentation

◆ Fft() [1/5]

static std::vector< ComplexNumber > vtkFFT::Fft ( const std::vector< ScalarNumber > & in )

static

Compute the one-dimensional DFT for complex input.

If input is scalars then the imaginary part is set to 0

input has n complex points output has n complex points in case of success and empty in case of failure

◆ Fft() [2/5]

static void vtkFFT::Fft	(	ScalarNumber *	input,
		std::size_t	size,
		ComplexNumber *	result
	)

static

Compute the one-dimensional DFT for complex input.

If input is scalars then the imaginary part is set to 0

input has n complex points output has n complex points in case of success and empty in case of failure

◆ Fft() [3/5]

static std::vector< ComplexNumber > vtkFFT::Fft ( const std::vector< ComplexNumber > & in )

static

Compute the one-dimensional DFT for complex input.

If input is scalars then the imaginary part is set to 0

input has n complex points output has n complex points in case of success and empty in case of failure

◆ Fft() [4/5]

static void vtkFFT::Fft	(	ComplexNumber *	input,
		std::size_t	size,
		ComplexNumber *	result
	)

static

Compute the one-dimensional DFT for complex input.

If input is scalars then the imaginary part is set to 0

input has n complex points output has n complex points in case of success and empty in case of failure

◆ Fft() [5/5]

static vtkSmartPointer< vtkScalarNumberArray > vtkFFT::Fft ( vtkScalarNumberArray * input )

static

Compute the one-dimensional DFT for complex input.

If input is scalars then the imaginary part is set to 0

input has n complex points output has n complex points in case of success and empty in case of failure

◆ RFft() [1/4]

static std::vector< ComplexNumber > vtkFFT::RFft ( const std::vector< ScalarNumber > & in )

static

Compute the one-dimensional DFT for real input.

input has n scalar points output has (n/2) + 1 complex points in case of success and empty in case of failure

◆ RFft() [2/4]

static void vtkFFT::RFft	(	ScalarNumber *	input,
		std::size_t	size,
		ComplexNumber *	result
	)

static

Compute the one-dimensional DFT for real input.

input has n scalar points output has (n/2) + 1 complex points in case of success and empty in case of failure

◆ RFft() [3/4]

static vtkSmartPointer< vtkScalarNumberArray > vtkFFT::RFft ( vtkScalarNumberArray * input )

static

Compute the one-dimensional DFT for real input.

input has n scalar points output has (n/2) + 1 complex points in case of success and empty in case of failure

◆ IFft()

static std::vector< ComplexNumber > vtkFFT::IFft ( const std::vector< ComplexNumber > & in )

static

Compute the inverse of Fft.

The input should be ordered in the same way as is returned by Fft, i.e.,

in[0] should contain the zero frequency term,
in[1:n//2] should contain the positive-frequency terms,
in[n//2 + 1:] should contain the negative-frequency terms.

input has n complex points output has n scalar points in case of success and empty in case of failure

◆ IRFft()

static std::vector< ScalarNumber > vtkFFT::IRFft ( const std::vector< ComplexNumber > & in )

static

Compute the inverse of RFft.

The input is expected to be in the form returned by Rfft, i.e. the real zero-frequency term followed by the complex positive frequency terms in order of increasing frequency.

input has (n/2) + 1 complex points output has n scalar points in case of success and empty in case of failure

◆ Abs()

vtkFFT::ScalarNumber vtkFFT::Abs ( const ComplexNumber & in )

inlinestatic

Return the absolute value (also known as norm, modulus, or magnitude) of complex number.

Definition at line 493 of file vtkFFT.h.

◆ SquaredAbs()

vtkFFT::ScalarNumber vtkFFT::SquaredAbs ( const ComplexNumber & in )

inlinestatic

Return the squared absolute value of the complex number.

Definition at line 499 of file vtkFFT.h.

◆ Conjugate()

vtkFFT::ComplexNumber vtkFFT::Conjugate ( const ComplexNumber & in )

inlinestatic

Return the conjugate of the given complex number.

Definition at line 505 of file vtkFFT.h.

◆ FftFreq()

static std::vector< ScalarNumber > vtkFFT::FftFreq	(	int	windowLength,
		double	sampleSpacing
	)

static

Return the DFT sample frequencies.

Output has windowLength size.

◆ RFftFreq()

static std::vector< ScalarNumber > vtkFFT::RFftFreq	(	int	windowLength,
		double	sampleSpacing
	)

static

Return the DFT sample frequencies for the real version of the dft (see Rfft).

Output has (windowLength / 2) + 1 size.

◆ GetOctaveFrequencyRange()

static std::array< double, 2 > vtkFFT::GetOctaveFrequencyRange	(	Octave	octave,
		OctaveSubdivision	octaveSubdivision = `OctaveSubdivision::Full`,
		bool	baseTwo = `true`
	)

static

Return lower and upper frequency from a octave band number / nominal midband frequency.

Parameters

[in]	octave	octave band number associated to nominal midband frequency
[in]	octaveSubdivision	(optional) which subdivision of octave wanted (default: Full)
[in]	baseTwo	(optional) whether to compute it using base-2 or base-10 (default: base-2) cf. "ANSI S1.11: Specification for Octave, Half-Octave, and Third Octave Band Filter Sets".

◆ OverlappingFft() [1/2]

template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>

static std::vector< ComplexNumber > vtkFFT::OverlappingFft	(	const std::vector< T > &	signal,
		const std::vector< TW > &	window,
		std::size_t	noverlap,
		bool	detrend,
		bool	onesided,
		unsigned int *	shape = `nullptr`
	)

static

Compute consecutive Fourier transforms Welch method without averaging nor scaling the result.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[out]	shape	if not `nullptr`, return the shape (n,m) of the result. `n` is the number of segment and `m` the number of samples per segment.

Returns: a 1D array that stores all resulting segment. For a shape (N,M), layout is (segment0_sample0, segment0_sample1, ..., segment0_sampleM, segment1_sample0, ... segmentN_sampleM)

◆ OverlappingFft() [2/2]

template<typename TW >

static vtkFFT::ComplexNumber * vtkFFT::OverlappingFft	(	vtkFFT::vtkScalarNumberArray *	signal,
		const std::vector< TW > &	window,
		std::size_t	noverlap,
		bool	detrend,
		bool	onesided,
		unsigned int *	shape = `nullptr`
	)

static

Compute consecutive Fourier transforms Welch method without averaging nor scaling the result.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[out]	shape	if not `nullptr`, return the shape (n,m) of the result. `n` is the number of segment and `m` the number of samples per segment.

Returns: a 1D array that stores all resulting segment. For a shape (N,M), layout is (segment0_sample0, segment0_sample1, ..., segment0_sampleM, segment1_sample0, ... segmentN_sampleM)

◆ Spectrogram() [1/2]

template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>

static std::vector< ComplexNumber > vtkFFT::Spectrogram	(	const std::vector< T > &	signal,
		const std::vector< TW > &	window,
		double	sampleRate,
		int	noverlap,
		bool	detrend,
		bool	onesided,
		vtkFFT::Scaling	scaling,
		vtkFFT::SpectralMode	mode,
		unsigned int *	shape = `nullptr`,
		bool	transpose = `false`
	)

static

Compute a spectrogram with consecutive Fourier transforms using Welch method.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	sampleRate	sample rate of the input signal
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[in]	scaling	can be either Cross Spectral Density (V^2/Hz) or Cross Spectrum (V^2)
[in]	mode	determine which type of value ares returned. It is very dependent to how you want to use the result afterwards.
[out]	shape	if not `nullptr`, return the shape (n,m) of the result. `n` is the number of segment and `m` the number of samples per segment. Shape is inverted if `transpose` is true.
[in]	transpose	allows to transpose the resulting the resulting matrix into something of shape (m, n)

Returns: a 1D array that stores all resulting segment. For a shape (N,M), layout is (segment0_sample0, segment0_sample1, ..., segment0_sampleM, segment1_sample0, ... segmentN_sampleM)

◆ Spectrogram() [2/2]

template<typename TW >

static vtkSmartPointer< vtkFFT::vtkScalarNumberArray > vtkFFT::Spectrogram	(	vtkFFT::vtkScalarNumberArray *	signal,
		const std::vector< TW > &	window,
		double	sampleRate,
		int	noverlap,
		bool	detrend,
		bool	onesided,
		vtkFFT::Scaling	scaling,
		vtkFFT::SpectralMode	mode,
		unsigned int *	shape = `nullptr`,
		bool	transpose = `false`
	)

static

Compute a spectrogram with consecutive Fourier transforms using Welch method.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	sampleRate	sample rate of the input signal
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[in]	scaling	can be either Cross Spectral Density (V^2/Hz) or Cross Spectrum (V^2)
[in]	mode	determine which type of value ares returned. It is very dependent to how you want to use the result afterwards.
[out]	shape	if not `nullptr`, return the shape (n,m) of the result. `n` is the number of segment and `m` the number of samples per segment. Shape is inverted if `transpose` is true.
[in]	transpose	allows to transpose the resulting the resulting matrix into something of shape (m, n)

Returns: a 1D array that stores all resulting segment. For a shape (N,M), layout is (segment0_sample0, segment0_sample1, ..., segment0_sampleM, segment1_sample0, ... segmentN_sampleM)

◆ Csd() [1/2]

template<typename T , typename TW , typename std::enable_if< isFftType< T >::value >::type * = nullptr>

static std::vector< vtkFFT::ScalarNumber > vtkFFT::Csd	(	const std::vector< T > &	signal,
		const std::vector< TW > &	window,
		double	sampleRate,
		int	noverlap,
		bool	detrend,
		bool	onesided,
		vtkFFT::Scaling	scaling
	)

static

Compute the Cross Spectral Density of a given signal.

This is the optimized version for computing the csd of a single signal with itself. It uses Spectrogram behind the hood, and then average all resulting segments of the spectrogram.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	sampleRate	sample rate of the input signal
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[in]	scaling	can be either Cross Spectral Density (V^2/Hz) or Cross Spectrum (V^2)

Returns: a 1D array containing the resulting cross spectral density or spectrum.

See vtkFFT::Spectrogram

◆ Csd() [2/2]

template<typename TW >

static vtkSmartPointer< vtkFFT::vtkScalarNumberArray > vtkFFT::Csd	(	vtkScalarNumberArray *	signal,
		const std::vector< TW > &	window,
		double	sampleRate,
		int	noverlap,
		bool	detrend,
		bool	onesided,
		vtkFFT::Scaling	scaling
	)

static

Compute the Cross Spectral Density of a given signal.

This is the optimized version for computing the csd of a single signal with itself. It uses Spectrogram behind the hood, and then average all resulting segments of the spectrogram.

Parameters

[in]	signal	the input signal
[in]	window	the window to use per segment. Its size defines the size of FFT and thus the size of the output.
[in]	sampleRate	sample rate of the input signal
[in]	noverlap	number of samples that will overlap between two segment
[in]	detrend	if true then each segment will be detrend using the mean value of the segment before applying the FFT.
[in]	onesided	if true return a one-sided spectrum for real data. If input is copmlex then this option will be ignored.
[in]	scaling	can be either Cross Spectral Density (V^2/Hz) or Cross Spectrum (V^2)

Returns: a 1D array containing the resulting cross spectral density or spectrum.

See vtkFFT::Spectrogram

◆ Transpose()

template<typename T >

static void vtkFFT::Transpose	(	T *	data,
		unsigned int *	shape
	)

static

Transpose in place an inlined 2D matrix.

This algorithm is not optimized for square matrices but is generic. This will also effectively swap shape values. Worst case complexity is : O( (shape[0]*shape[1])^3/2 )

XXX: some fft libraries such as FFTW already propose functions to do that. This should be taken into account if the backend is changed at some point.

XXX: An optimized version could be implemented for square matrices

◆ HanningGenerator()

double vtkFFT::HanningGenerator	(	std::size_t	x,
		std::size_t	size
	)

inlinestatic

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 511 of file vtkFFT.h.

◆ BartlettGenerator()

double vtkFFT::BartlettGenerator	(	std::size_t	x,
		std::size_t	size
	)

inlinestatic

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 517 of file vtkFFT.h.

◆ SineGenerator()

double vtkFFT::SineGenerator	(	std::size_t	x,
		std::size_t	size
	)

inlinestatic

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 523 of file vtkFFT.h.

◆ BlackmanGenerator()

double vtkFFT::BlackmanGenerator	(	std::size_t	x,
		std::size_t	size
	)

inlinestatic

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 529 of file vtkFFT.h.

◆ RectangularGenerator()

double vtkFFT::RectangularGenerator	(	std::size_t	x,
		std::size_t	size
	)

inlinestatic

Window generator functions.

Implementation only needs to be valid for x E [0; size / 2] because kernels are symmetric by definitions. This point is very important for some kernels like Bartlett for example.

Warning: Most generators need size > 1 !

Can be used with GenerateKernel1D and GenerateKernel2D for generating full kernels.

Definition at line 536 of file vtkFFT.h.

◆ GenerateKernel1D()

template<typename T >

void vtkFFT::GenerateKernel1D	(	T *	kernel,
		std::size_t	n,
		WindowGenerator	generator
	)

static

Given a window generator function, create a symmetric 1D kernel.

kernel is the pointer to the raw data array

Definition at line 543 of file vtkFFT.h.

◆ GenerateKernel2D()

template<typename T >

void vtkFFT::GenerateKernel2D	(	T *	kernel,
		std::size_t	n,
		std::size_t	m,
		WindowGenerator	generator
	)

static

Given a window generator function, create a symmetric 2D kernel.

kernel is the pointer to the raw 2D data array.

Definition at line 554 of file vtkFFT.h.

◆ New()

static vtkFFT * vtkFFT::New ( )

static

◆ IsTypeOf()

static vtkTypeBool vtkFFT::IsTypeOf ( const char * type )

static

◆ IsA()

virtual vtkTypeBool vtkFFT::IsA ( const char * name )

virtual

Return 1 if this class is the same type of (or a subclass of) the named class.

Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkObjectBase.

◆ SafeDownCast()

static vtkFFT * vtkFFT::SafeDownCast ( vtkObjectBase * o )

static

◆ NewInstanceInternal()

virtual vtkObjectBase * vtkFFT::NewInstanceInternal ( ) const

protectedvirtual

◆ NewInstance()

vtkFFT * vtkFFT::NewInstance ( ) const

◆ PrintSelf()

void vtkFFT::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)

overridevirtual

Methods invoked by print to print information about the object including superclasses.

Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkObjectBase.

◆ Zero() [1/2]

template<typename T >

constexpr T vtkFFT::Zero

staticconstexprprotected

Templated zero value, specialized for vtkFFT::ComplexNumber.

Definition at line 447 of file vtkFFT.h.

◆ ComputeScaling()

template<typename InputIt >

static std::iterator_traits< InputIt >::value_type vtkFFT::ComputeScaling	(	InputIt	begin,
		InputIt	end,
		Scaling	scaling,
		double	fs
	)

staticprotected

For a given window defined by begin and end, compute the scaling needed to apply to the resulting FFT.

Used in the Spectrogram function.

◆ PreprocessAndDispatchFft()

template<typename T , typename TW >

static void vtkFFT::PreprocessAndDispatchFft	(	const T *	segment,
		const std::vector< TW > &	window,
		bool	detrend,
		bool	onesided,
		vtkFFT::ComplexNumber *	result
	)

staticprotected

Dispatch the signal to the right FFT function according to the given parameters.

Also detrend the signal and multiply it by the window. Used in the OverlappingFft function.

◆ RFft() [4/4]

static void vtkFFT::RFft	(	ComplexNumber *	input,
		std::size_t	size,
		ComplexNumber *	result
	)

staticprotected

XXX(c++17): This function should NOT exist and is here just for the sake template unfolding purposes.

As long we don't have constexrp if this is the easier way to deal with it.

Warning: this function will always throw an error

See also: PreprocessAndDispatchFft

◆ ScaleFft()

template<typename TW >

static void vtkFFT::ScaleFft	(	ComplexNumber *	fft,
		unsigned int	shape[2],
		const std::vector< TW > &	window,
		double	sampleRate,
		bool	onesided,
		vtkFFT::Scaling	scaling,
		vtkFFT::SpectralMode	mode
	)

staticprotected

Scale a fft according to its window and some mode.

Used in the Spectrogram function.

◆ Zero() [2/2]

template<>

constexpr vtkFFT::ComplexNumber vtkFFT::Zero ( )

constexpr

Definition at line 452 of file vtkFFT.h.

The documentation for this class was generated from the following file:

Common/Math/vtkFFT.h

Classes

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ScalarNumber

◆ ComplexNumber

◆ vtkScalarNumberArray

◆ WindowGenerator

◆ Superclass

Member Enumeration Documentation

◆ Octave

◆ OctaveSubdivision

◆ Scaling

◆ SpectralMode

Constructor & Destructor Documentation

◆ vtkFFT()

◆ ~vtkFFT()

Member Function Documentation

◆ Fft() [1/5]

◆ Fft() [2/5]

◆ Fft() [3/5]

◆ Fft() [4/5]

◆ Fft() [5/5]

◆ RFft() [1/4]

◆ RFft() [2/4]

◆ RFft() [3/4]

◆ IFft()

◆ IRFft()

◆ Abs()

◆ SquaredAbs()

◆ Conjugate()

◆ FftFreq()

◆ RFftFreq()

◆ GetOctaveFrequencyRange()

◆ OverlappingFft() [1/2]

◆ OverlappingFft() [2/2]

◆ Spectrogram() [1/2]

◆ Spectrogram() [2/2]

◆ Csd() [1/2]

◆ Csd() [2/2]

◆ Transpose()

◆ HanningGenerator()

◆ BartlettGenerator()

◆ SineGenerator()

◆ BlackmanGenerator()

◆ RectangularGenerator()

◆ GenerateKernel1D()

◆ GenerateKernel2D()

◆ New()

◆ IsTypeOf()

◆ IsA()

◆ SafeDownCast()

◆ NewInstanceInternal()

◆ NewInstance()

◆ PrintSelf()

◆ Zero() [1/2]

◆ ComputeScaling()

◆ PreprocessAndDispatchFft()

◆ RFft() [4/4]

◆ ScaleFft()

◆ Zero() [2/2]