rft_genericrft_genericRftGenericRftGenericrft_generic (Operator)

Name

rft_genericrft_genericRftGenericRftGenericrft_generic — Compute the real-valued fast Fourier transform of an image.

Signature

Description

rft_genericrft_genericRftGenericRftGenericrft_generic computes the fast Fourier transform of the input image ImageImageImageimageimage. In contrast to fft_genericfft_genericFftGenericFftGenericfft_generic, fft_imagefft_imageFftImageFftImagefft_image, and fft_image_invfft_image_invFftImageInvFftImageInvfft_image_inv, the fact that the input image in the forward transform is a real-valued image (i.e., not a complex image) is used. In this case, the complex output image has a redundancy. The values in the right half of the image are the complex conjugates of the corresponding values in the left half of the image. Consequently, runtime and memory can be saved by only computing and storing the left half of the complex image.

The parameter ResultTypeResultTypeResultTyperesultTyperesult_type 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"), ResultTypeResultTypeResultTyperesultTyperesult_type must be set to 'complex'"complex""complex""complex""complex".

The parameter direction determines whether the transform should be performed to the frequency domain or back into the spatial domain. For DirectionDirectionDirectiondirectiondirection = 'to_freq'"to_freq""to_freq""to_freq""to_freq" the input image must have a real-valued type, i.e., a complex image may not be used as input. All image types that can be converted into an image of type real are supported. In this case, the output is a complex image of dimension (w/2+1)*h, where w and h are the width and height of the input image. In this mode, the exponent -1 is used in the transform (see fft_genericfft_genericFftGenericFftGenericfft_generic). For DirectionDirectionDirectiondirectiondirection = 'from_freq'"from_freq""from_freq""from_freq""from_freq", the input image must be complex. In this case, the size of the input image is insufficient to determine the size of the output image. This must be done by setting WidthWidthWidthwidthwidth to a valid value, i.e., to 2*w-2 or 2*w-1, where w is the width of the complex image. In this mode, the exponent 1 is used in the transform.

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 user must ensure the consistent use of the parameters. This means that the normalizing factors used for the forward and backward transform must yield w*h when multiplied.

Attention

The transformation is always performed for the entire image, i.e., the domain of the image is ignored.

Execution Information

• 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 channel level.
• Automatically parallelized on internal data level.

Parameters

Result

rft_genericrft_genericRftGenericRftGenericrft_generic 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>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>). If necessary, an exception is raised.

Possible Predecessors

optimize_rft_speedoptimize_rft_speedOptimizeRftSpeedOptimizeRftSpeedoptimize_rft_speed, read_fft_optimization_dataread_fft_optimization_dataReadFftOptimizationDataReadFftOptimizationDataread_fft_optimization_data

Possible Successors

convol_fftconvol_fftConvolFftConvolFftconvol_fft, correlation_fftcorrelation_fftCorrelationFftCorrelationFftcorrelation_fft, phase_correlation_fftphase_correlation_fftPhaseCorrelationFftPhaseCorrelationFftphase_correlation_fft, convert_image_typeconvert_image_typeConvertImageTypeConvertImageTypeconvert_image_type, power_bytepower_bytePowerBytePowerBytepower_byte, power_realpower_realPowerRealPowerRealpower_real, power_lnpower_lnPowerLnPowerLnpower_ln, phase_degphase_degPhaseDegPhaseDegphase_deg, phase_radphase_radPhaseRadPhaseRadphase_rad

Alternatives

fft_genericfft_genericFftGenericFftGenericfft_generic, fft_imagefft_imageFftImageFftImagefft_image, fft_image_invfft_image_invFftImageInvFftImageInvfft_image_inv

Module

Foundation