Non-equispaced fast Fourier transform (NFFT) More...

#include <NFFT.h>

Public Member Functions
	NFFT (size_t m, size_t n, size_t fft_size)
	NFFT Constructor. More...

void	execute (const std::valarray< std::complex< T >> &spectrum, const std::valarray< double > &times, std::valarray< std::complex< T >> &out)
	Execute a transform. More...

void	execute (size_t isize, size_t istride, const std::complex< T > spectrum, size_t tsize, size_t tstride, const double times, size_t osize, size_t ostride, std::complex< T > *out)
	Execute a transform (raw pointer interface). More...

void	execute_adjoint (const std::valarray< std::complex< T >> &time_series, const std::valarray< double > &times, std::valarray< std::complex< T >> &spectrum)
	Execute an adjoint transform. More...

void	execute_adjoint (size_t isize, size_t istride, const std::complex< T > time_series, size_t tsize, size_t tstride, const double times, size_t osize, size_t ostride, std::complex< T > *spectrum)
	Execute an adjoint transform (raw pointer interface). More...

void	set_spectrum (const std::valarray< std::complex< T >> &x)
	Ingest a spectrum for transform. More...

void	set_spectrum (size_t size, size_t stride, const std::complex< T > *x)
	Ingest a spectrum for transform (raw pointer interface). More...

std::complex< T >	interp (double t) const
	Interpolate the transformed signal. More...

size_t	size_kernel () const

size_t	size_spectrum () const

size_t	size_transform () const

Detailed Description

template<class>
class isce3::signal::NFFT< class >

Non-equispaced fast Fourier transform (NFFT)

Class implementing NFFT algorithm described in [4] . It takes a uniformly sampled spectrum and produces time-domain samples at arbitrary locations.

Compared to the TU Chemnitz implementation there are some differences in conventions intended to make things simpler in the SAR context:

Sign conventions. NFFT.execute() uses a positive phase (backward), while NFFT.execute_adjoint() uses a negative phase (forward). This consistent with uses where the frequency spectrum is uniformly sampled and the time domain is not.
Order of spectra. Spectra are expected to be in FFTW order, e.g. low frequencies at the ends and high frequencies in the middle.
Scaling of time/frequency. Locations are specified as sample numbers (at rate consistent with spectrum size) instead of the unit torus.
Sample locations do not need to be specified in advance. You can use NFFT.set_spectrum and then NFFT.interp all the points you want on the fly. The NFFT.execute convenience function combines these.

Constructor & Destructor Documentation

template<class T >

isce3::signal::NFFT< T >::NFFT	(	size_t	m,
		size_t	n,
		size_t	fft_size
	)

NFFT Constructor.

Parameters

[in]	m	Interpolation kernel size parameter (width=2*m+1).
[in]	n	Length of spectrum.
[in]	fft_size	Transform size (> n).

Member Function Documentation

template<class T >

void isce3::signal::NFFT< T >::execute	(	const std::valarray< std::complex< T >> &	spectrum,
		const std::valarray< double > &	times,
		std::valarray< std::complex< T >> &	out
	)

Execute a transform.

Equivalent to

\[ f_j = \frac{1}{N} \sum_{k=-\frac{N}{2}}^{\frac{N}{2}-1} \hat{f}_k \exp(+2\pi i k t_j / N) \]

Where \( N \) is the size of the spectrum.

Parameters

[in]	spectrum	Signal to transform, in FFTW order.
[in]	times	Desired sample locations in [0:n)
[out]	out	Storage for output signal, same length as times.

Equivalent to set_spectrum and out[i]=NFFT::interp(times[i]).

See Also: set_spectrum; interp

template<class T >

void isce3::signal::NFFT< T >::execute	(	size_t	isize,
		size_t	istride,
		const std::complex< T > *	spectrum,
		size_t	tsize,
		size_t	tstride,
		const double *	times,
		size_t	osize,
		size_t	ostride,
		std::complex< T > *	out
	)

Execute a transform (raw pointer interface).

Parameters

[in]	isize	Length of spectrum (should be == n)
[in]	istride	Stride between elements of spectrum.
[in]	spectrum	Signal to transform, in FFTW order.
[in]	tsize	Number of output time samples.
[in]	tstride	Stride between elements of time array.
[in]	times	Desired sample locations in [0:n)
[in]	tsize	Number of output samples (should be == tsize).
[in]	tstride	Stride between elements of output array.
[out]	out	Storage for output signal.

Equivalent to set_spectrum and out[i]=NFFT::interp(times[i]).

See Also: set_spectrum; interp

template<class T >

void isce3::signal::NFFT< T >::execute_adjoint	(	const std::valarray< std::complex< T >> &	time_series,
		const std::valarray< double > &	times,
		std::valarray< std::complex< T >> &	spectrum
	)

Execute an adjoint transform.

Equivalent to

\[ \hat{f}_k = \sum_{j=0}^{M-1} f_j \exp(-2\pi i k t_j / N) \]

Where \( M \) is the number of time samples and \( N \) is the size of the spectrum.

Parameters

[in]	time_series	Signal to transform.
[in]	times	Sample locations in [0:n) of input signal.
[out]	spectrum	Storage for output spectrum. Length should be equal to size_spectrum().

template<class T >

void isce3::signal::NFFT< T >::execute_adjoint	(	size_t	isize,
		size_t	istride,
		const std::complex< T > *	time_series,
		size_t	tsize,
		size_t	tstride,
		const double *	times,
		size_t	osize,
		size_t	ostride,
		std::complex< T > *	spectrum
	)

Execute an adjoint transform (raw pointer interface).

Parameters

[in]	isize	Length of input signal.
[in]	istride	Stride between elements of input signal.
[in]	time_series	Signal to transform.
[in]	tsize	Length of time vector. Should == isize.
[in]	tstride	Stride of time vector.
[in]	times	Sample locations in [0:n) of input signal.
[in]	osize	Length of output signal (== size_spectrum())
[in]	ostride	Stride between elements of output signal.
[out]	spectrum	Storage for output spectrum.

template<class T >

std::complex< T > isce3::signal::NFFT< T >::interp ( double t ) const

Interpolate the transformed signal.

Parameters

[in] t Location in [0,n) to sample the time-domain signal.

See Also: execute is an alternative strategy.; set_spectrum must be called first.

template<class T >

void isce3::signal::NFFT< T >::set_spectrum ( const std::valarray< std::complex< T >> & x )

Ingest a spectrum for transform.

Parameters

[in] x Spectrum to transform. Should be in FFTW order, e.g., [0:pi, -pi:0).

This function will filter, zero-pad, and transform the input data. After this you can call NFFT.interp.

See Also: execute Is an alternative strategy.; interp

template<class T >

void isce3::signal::NFFT< T >::set_spectrum	(	size_t	size,
		size_t	stride,
		const std::complex< T > *	x
	)

Ingest a spectrum for transform (raw pointer interface).

Parameters

[in]	size	Length of signal. Should be same as n in constructor or else zero-padding will be wrong.
[in]	stride	Stride between array elements.
[in]	x	Spectrum to transform. Should be in FFTW order, e.g., [0:pi, -pi:0).

This function will filter, zero-pad, and transform the input data. After this you can call the interp method.

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

isce/cxx/isce3/signal/forward.h
isce/cxx/isce3/signal/NFFT.h
isce/cxx/isce3/signal/NFFT.cpp

Public Member Functions

Detailed Description

template<class> class isce3::signal::NFFT< class >

Constructor & Destructor Documentation

Member Function Documentation

template<class>
class isce3::signal::NFFT< class >