fft_genericfft_genericfft_genericFftGenericFftGeneric (Operator)

Name

fft_genericfft_genericfft_genericFftGenericFftGeneric — Compute the fast Fourier transform of an image.

Signature

Description

fft_genericfft_genericfft_genericFftGenericFftGeneric computes the fast Fourier transform of the input image ImageImageImageImageimage. Because several definitions of the forward and reverse transforms exist in the literature, this operator allows the user to select the most convenient definition.

The general definition of a Fourier transform is as follows:

               M-1  N-1
               ---  ---
           1   \    \    s*2*pi*i*(k*m/M+l*n/N)
  F(m,n) = - * /    /   e                       * f(k,l)
           c   ---  ---
               k=0  l=0

Opinions vary on whether the sign s in the exponent should be set to 1 or -1 for the forward transform, i.e., the transform for going to the frequency domain. There is also disagreement on the magnitude of the normalizing factor c. This is sometimes set to 1 for the forward transform, sometimes to M*N, and sometimes (in case of the unitary FFT) to sqrt(M*N). Especially in image processing applications the DC term is shifted to the center of the image.

fft_genericfft_genericfft_genericFftGenericFftGeneric allows to select these choices individually. The parameter DirectionDirectionDirectionDirectiondirection allows to select the logical direction of the FFT. (This parameter is not unnecessary; it is needed to discern how to shift the image if the DC term should rest in the center of the image.) Possible values are 'to_freq'"to_freq""to_freq""to_freq""to_freq" and 'from_freq'"from_freq""from_freq""from_freq""from_freq". The parameter ExponentExponentExponentExponentexponent is used to determine the sign of the exponent. It can be set to 1 or -1. The normalizing factor can be set with NormNormNormNormnorm, and can take on the values 'none'"none""none""none""none", 'sqrt'"sqrt""sqrt""sqrt""sqrt" and 'n'"n""n""n""n". The parameter ModeModeModeModemode determines the location of the DC term of the FFT. It can be set to 'dc_center'"dc_center""dc_center""dc_center""dc_center" or 'dc_edge'"dc_edge""dc_edge""dc_edge""dc_edge".

In any case, the user must ensure the consistent use of the parameters. This means that the normalizing factors used for the forward and backward transform must yield M*N when multiplied, the exponents must be of opposite sign, and ModeModeModeModemode must be equal for both transforms.

A consistent combination is, for example '(to_freq,-1,n,dc_edge)'"(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)""(to_freq,-1,n,dc_edge)" for the forward transform and '(from_freq,1,none,dc_edge)'"(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)""(from_freq,1,none,dc_edge)" for the reverse transform. In this case, the FFT can be interpreted as interpolation with trigonometric basis functions. Another possible combination is '(to_freq,-1,sqrt,dc_center)'"(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)""(to_freq,-1,sqrt,dc_center)" and '(from_freq,1,sqrt,dc_center)'"(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)""(from_freq,1,sqrt,dc_center)".

The parameter ResultTypeResultTypeResultTypeResultTyperesultType can be used to specify the result image type of the reverse transform (DirectionDirectionDirectionDirectiondirection = 'from_freq'"from_freq""from_freq""from_freq""from_freq"). In the forward transform (DirectionDirectionDirectionDirectiondirection = 'to_freq'"to_freq""to_freq""to_freq""to_freq"), ResultTypeResultTypeResultTypeResultTyperesultType must be set to 'complex'"complex""complex""complex""complex".

Attention

The filtering is always done on the entire image, i.e., the region of the image is ignored.

Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.
• Automatically parallelized on internal data level.

Parameters

Example (C)

/* simulation of fft */
my_fft(Hobject In, Hobject *Out)
{
  fft_generic(In,Out,"to_freq",-1,"sqrt","dc_center","complex");
}

/* simulation of fft_image_inv */
my_fft_image_inv(Hobject In, Hobject *Out)
{
  fft_generic(In,&Out,"from_freq",1,"sqrt","dc_center","byte");
}

Result

fft_genericfft_genericfft_genericFftGenericFftGeneric returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised.

Possible Predecessors

optimize_fft_speedoptimize_fft_speedoptimize_fft_speedOptimizeFftSpeedOptimizeFftSpeed, read_fft_optimization_dataread_fft_optimization_dataread_fft_optimization_dataReadFftOptimizationDataReadFftOptimizationData

Possible Successors

convol_fftconvol_fftconvol_fftConvolFftConvolFft, convol_gaborconvol_gaborconvol_gaborConvolGaborConvolGabor, convert_image_typeconvert_image_typeconvert_image_typeConvertImageTypeConvertImageType, power_bytepower_bytepower_bytePowerBytePowerByte, power_realpower_realpower_realPowerRealPowerReal, power_lnpower_lnpower_lnPowerLnPowerLn, phase_degphase_degphase_degPhaseDegPhaseDeg, phase_radphase_radphase_radPhaseRadPhaseRad, energy_gaborenergy_gaborenergy_gaborEnergyGaborEnergyGabor

Alternatives

fft_imagefft_imagefft_imageFftImageFftImage, fft_image_invfft_image_invfft_image_invFftImageInvFftImageInv, rft_genericrft_genericrft_genericRftGenericRftGeneric

Module

Foundation