rft_generic🔗
Short description🔗
rft_generic — Compute the real-valued fast Fourier transform of an image.
Signature🔗
rft_generic( image Image, out image ImageFFT, string Direction, string Norm, string ResultType, integer Width )
Description🔗
rft_generic computes the fast Fourier transform of the input
image Image. In contrast to fft_generic,
fft_image, and fft_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 ResultType can be used to specify the result
image type of the reverse transform (Direction \(=\)
'from_freq'). In the forward transform (Direction
\(=\) 'to_freq'), ResultType must be set to
'complex'.
The parameter direction determines whether the transform should be
performed to the frequency domain or back into the spatial domain.
For Direction \(=\) '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_generic). For
Direction \(=\) '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 Width to a valid value, i.e., to 2w-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 Norm, and can take
on the values 'none', 'sqrt' and '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🔗
Execution information
-
Multithreading type: reentrant (runs in parallel with non-exclusive operators).
-
Multithreading scope: global (may be called from any thread).
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Automatically parallelized on tuple level.
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Automatically parallelized on channel level.
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Automatically parallelized on internal data level.
Parameters🔗
Image (input_object) (multichannel-)image(-array) → object (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real / complex)
Input image.
ImageFFT (output_object) image(-array) → object (byte / direction / cyclic / int1 / int2 / uint2 / int4 / real / complex)
Fourier-transformed image.
Direction (input_control) string → (string)
Calculate forward or reverse transform.
Default: 'to_freq'
List of values: 'from_freq', 'to_freq'
Norm (input_control) string → (string)
Normalizing factor of the transform.
Default: 'sqrt'
List of values: 'n', 'none', 'sqrt'
ResultType (input_control) string → (string)
Image type of the output image.
Default: 'complex'
List of values: 'byte', 'complex', 'cyclic', 'direction', 'int1', 'int2', 'int4', 'real', 'uint2'
Width (input_control) integer → (integer)
Width of the image for which the runtime should be optimized.
Default: 512
Suggested values: 128, 160, 192, 256, 320, 384, 512, 640, 768, 1024, 2048
Result🔗
rft_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>:). If necessary,
an exception is raised.
Combinations with other operators🔗
Combinations
Possible predecessors
optimize_rft_speed, read_fft_optimization_data
Possible successors
convol_fft, correlation_fft, phase_correlation_fft, convert_image_type, power_byte, power_real, power_ln, phase_deg, phase_rad
Alternatives
Module🔗
Foundation