SF_FFT

Description

SciFortran module for Fourier transform

Quick access

Routines:

cfft_1d_backward(), cfft_1d_ex(), cfft_1d_forward(), cfft_1d_ishift(), cfft_1d_shift(), cfft_2d_backward(), cfft_2d_forward(), cfft_nd_backward(), cfft_nd_forward(), cosft(), cosftn(), cost_1d_backward(), cost_1d_forward(), cost_nd_backward(), cost_nd_forward(), fft(), fft2(), fft_farray(), fft_fmax(), fft_signal(), fft_tarray(), fft_tmax(), fftex(), fftn(), fftshift(), ft_direct(), ft_inverse(), icosft(), icosftn(), ifft(), ifft2(), ifft_signal(), ifftn(), ifftshift(), isinft(), isinftn(), itfft(), rfft_1d_backward(), rfft_1d_ex(), rfft_1d_forward(), rfft_1d_ishift(), rfft_1d_shift(), rfft_2d_backward(), rfft_2d_forward(), rfft_nd_backward(), rfft_nd_forward(), sinft(), sinftn(), sint_1d_backward(), sint_1d_forward(), sint_nd_backward(), sint_nd_forward(), tfft()

Used modules

Subroutines and functions

interface  sf_fft_fftpack/ft_direct(ft, t, w)

This function evaluates the direct Fourier transform of a discretized function from time to frequency domain. Takes as input a discretized function \(ft_{i}\) on a set of time points \(t_{i}\) and a set of frequencies \(w_{j}\) and returns a discretized function \(fw_{j}\) = simps \((ft_{i} \cdot e^{-i 2\pi w_{j}t_{i}}, t_{1}, t_{N})\) , where N=size(t)

Parameters:

  • ft (•) [real/complex, in,required] – Dicretized function to transform (time domain)

  • t (size(ft)) [real, in] – Discretized time points

  • w (•) [real, in] – Discretized frequency points

Result:

fw (size(w)) [real/complex] – Discretized Fourier-transform function (frequency domain)

interface  sf_fft_fftpack/ft_inverse(fw, t, w)

This function evaluates the inverse Fourier transform of a discretized function from frequency to time domain. Takes as input a discretized function \(fw_{i}\) on a set of time points \(w_{i}\) and a set of frequencies \(t_{j}\) and returns a discretized function \(ft_{j}\) = simps \((fw_{i} \cdot e^{i 2\pi t_{j}w_{i}}, w_{1}, w_{N})\) , where N=size(w)

Parameters:

  • fw (•) [real/complex, in,required] – Dicretized function to transform (frequency domain)

  • t (•) [real, in] – Discretized time points

  • w (size(fw)) [real, in] – Discretized frequency points

Result:

ft (size(t)) [real/complex] – Discretized Fourier-transform function (time domain)

interface  sf_fft_fftpack/fft_signal(ft, dt)

This function evaluates the fast Fourier transform of a discretized function ft . It returns fw = dt · tfft ( ft )

Parameters:

  • ft (•) [real/complex] – Time-domain function

  • dt [real] – Time step

Result:

fw (size(ft)) [real/complex] – Frequency-domain function

interface  sf_fft_fftpack/ifft_signal(fw, dt)

This function evaluates the inverse fast Fourier transform of a discretized function fw . It returns ft = itfft ( fw ) / ft

Parameters:

  • fw (•) [real/complex] – Frequency-domain function

  • dt [real] – Time step

Result:

ft (size(fw)) [real/complex] – Time-domain function

interface  sf_fft_fftpack/tfft(func_in[, func_out])
Parameters:

func_in (•) [real/complex, in,required]

Options:

func_out (size(func_in)) [real/complex]

interface  sf_fft_fftpack/itfft(func_in[, func_out])
Parameters:

func_in (•) [real/complex, in,required]

Options:

func_out (size(func_in)) [real/complex]

interface  sf_fft_fftpack/fft(func)

This subroutine evaluates the forward 1-dimensional FFT of an array of lenght N using the FFTPACK 5.1 routines rfft1i + rfft1f for the real case and cfft1i + cfft1f for the complex case. These are called with the parameters

  • lensav = N + int( log(dble(N))/log(2.d0) ) + 4

  • lenwrk = N

  • lenr = N

  • inc = 1

The subroutine modifies the input array to contain

  • [y(0), y(1), ..., y(N/2),     y(-N/2+1), ...,   y(-1)] if N is even

  • [y(0), y(1), ..., y((N-1)/2), y(-(N-1)/2), ..., y(-1)] if N is odd

where

\(y(j) = \sum_{k=0}^{N-1} x(k) \cdot e^{-i 2\pi/N \cdot j \cdot k}\)

for \(j \in [0,N-1]\)

Parameters:

func (•) [real/complex, inout] – Input/output array of size N

interface  sf_fft_fftpack/ifft(func)

This subroutine evaluates the backward 1-dimensional FFT of an array of lenght N using the FFTPACK 5.1 routines rfft1i + rfft1b for the real case and cfft1i + cfft1b for the complex case. These are called with the parameters

  • lensav = N + int( log(dble(N))/log(2.d0) ) + 4

  • lenwrk = N

  • lenr = N

  • inc = 1

The subroutine modifies the input array to contain

  • [y(0), y(1), ..., y(N/2),     y(-N/2+1), ...,   y(-1)] if N is even

  • [y(0), y(1), ..., y((N-1)/2), y(-(N-1)/2), ..., y(-1)] if N is odd

where

\(y(j) = \sum_{k=-N/2}^{N/2-1} x(k) \cdot a^{i 2\pi/N \cdot j \cdot k}\)

for \(j \in [0,N-1]\)

Parameters:

func (•) [real/complex, inout]

interface  sf_fft_fftpack/fft2(func)
Parameters:

func (•, •) [real/complex, inout]

interface  sf_fft_fftpack/ifft2(func)
Parameters:

func (•, •) [real/complex, inout]

interface  sf_fft_fftpack/fftn(func, n, lot)
Parameters:

  • func (•) [real/complex, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/ifftn(func, n, lot)
Parameters:

  • func (•) [real/complex, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/cosft(func)
Parameters:

func (•) [real, inout]

interface  sf_fft_fftpack/icosft(func)
Parameters:

func (•) [real, inout]

interface  sf_fft_fftpack/cosftn(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/icosftn(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/sinft(func)
Parameters:

func (•) [real, inout]

interface  sf_fft_fftpack/isinft(func)
Parameters:

func (•) [real, inout]

interface  sf_fft_fftpack/sinftn(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/isinftn(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

interface  sf_fft_fftpack/fftshift(fin)
Parameters:

fin (•) [real/complex]

Result:

fout (size(fin)) [real/complex]

interface  sf_fft_fftpack/ifftshift(fin)
Parameters:

fin (•) [real/complex]

Result:

fout (size(fin)) [real/complex]

interface  sf_fft_fftpack/fftex(func)
Parameters:

func (•) [real/complex]

subroutine  sf_fft_fftpack/rfft_1d_forward(func)
Parameters:

func (•) [real, inout] – Input/output array of size N

subroutine  sf_fft_fftpack/cfft_1d_forward(func)
Parameters:

func (•) [complex, inout]

subroutine  sf_fft_fftpack/rfft_2d_forward(func)
Parameters:

func (•, •) [real, inout]

subroutine  sf_fft_fftpack/cfft_2d_forward(func)
Parameters:

func (•, •) [complex, inout]

subroutine  sf_fft_fftpack/rfft_nd_forward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/cfft_nd_forward(func, n, lot)
Parameters:

  • func (•) [complex, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/cost_1d_forward(func)
Parameters:

func (•) [real, inout]

subroutine  sf_fft_fftpack/sint_1d_forward(func)
Parameters:

func (•) [real, inout]

subroutine  sf_fft_fftpack/cost_nd_forward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/sint_nd_forward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/rfft_1d_backward(func)
Parameters:

func (•) [real, inout]

subroutine  sf_fft_fftpack/cfft_1d_backward(func)
Parameters:

func (•) [complex, inout]

subroutine  sf_fft_fftpack/rfft_2d_backward(func)
Parameters:

func (•, •) [real, inout]

subroutine  sf_fft_fftpack/cfft_2d_backward(func)
Parameters:

func (•, •) [complex, inout]

subroutine  sf_fft_fftpack/rfft_nd_backward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/cfft_nd_backward(func, n, lot)
Parameters:

  • func (•) [complex, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/cost_1d_backward(func)
Parameters:

func (•) [real, inout]

subroutine  sf_fft_fftpack/sint_1d_backward(func)
Parameters:

func (•) [real, inout]

subroutine  sf_fft_fftpack/cost_nd_backward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

subroutine  sf_fft_fftpack/sint_nd_backward(func, n, lot)
Parameters:

  • func (•) [real, inout]

  • n [integer, in]

  • lot [integer, in]

function  sf_fft_fftpack/rfft_1d_shift(fin)
Parameters:

fin (•) [real]

Result:

fout (size(fin)) [real]

function  sf_fft_fftpack/cfft_1d_shift(fin)
Parameters:

fin (•) [complex]

Result:

fout (size(fin)) [complex]

function  sf_fft_fftpack/rfft_1d_ishift(fin)
Parameters:

fin (•) [real]

Result:

fout (size(fin)) [real]

function  sf_fft_fftpack/cfft_1d_ishift(fin)
Parameters:

fin (•) [complex]

Result:

fout (size(fin)) [complex]

subroutine  sf_fft_fftpack/rfft_1d_ex(func)
Parameters:

func (•) [real]

subroutine  sf_fft_fftpack/cfft_1d_ex(func)
Parameters:

func (•) [complex]

function  sf_fft_fftpack/fft_tmax(l, dt)
Parameters:

  • l [integer]

  • dt [real]

Result:

fft_tmax [real]

function  sf_fft_fftpack/fft_fmax(l, dt)
Parameters:

  • l [integer]

  • dt [real]

Result:

fft_fmax [real]

function  sf_fft_fftpack/fft_tarray(l, dt)
Parameters:

  • l [integer]

  • dt [real]

Result:

time (l) [real]

function  sf_fft_fftpack/fft_farray(l, dt[, df])
Parameters:

  • l [integer]

  • dt [real]

Options:

df [real]

Result:

freq (l) [real]