FTI

Description

Converts two-dimensional frequency domain data to spatial imagery data using one of the following inverse transformations: Fourier, Hadamard, Walsh, or Cosine.

Parameters

Name	Type	Length	Value range
Input: Input frequency domain channel(s) *	Raster port	1 - 2
Output *	Integer	1 - 1
X Offset	Integer	0 - 4
Y Offset	Integer	0 - 4
X Size	Integer	0 - 4
Y Size	Integer	0 - 4
Transformation Type	String	3 - 1	FIR | FMP | WAL | HAD | COS Default: FIR
Report	String	0 - 192	See parameter description

* Required parameter

Parameter descriptions

Input: Input frequency domain channel(s)

Specifies the input frequency domain channel(s) to be transformed to the spatial domain.

Output

Specifies the output channel to receive the spatial domain data; that is, the result of the transformed image data. Complex-valued output channels are supported.

X Offset

In conjunction with the Y Offset parameter, specifies the horizontal offset of the raster window that is read from the input image.

X Offset and Y Offset define the upper-left starting pixel coordinates of the window.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Y Offset

In conjunction with the X Offset parameter, specifies the vertical offset of the raster window that is read from the input image.

X Offset and Y Offset define the upper-left starting pixel coordinates of the window.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

X Size

In conjunction with the Y Size parameter, specifies the size of the raster window that is read from the input image.

X Size is the number of pixels that define the window width.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Y Size

In conjunction with the X Size parameter, specifies the size of the raster window that is read from the input image.

Y Size is the number of lines that define the window height.

If X Offset, Y Offset, X Size, and Y Size are not specified, the entire image is processed by default.

Transformation Type

Specifies the type of transformation to perform.

Report

Specifies where to direct the generated report.

Available options are:

• LOG: generates a report on the terminal (default)
• <modulename.RPT>: appends a report to the module's RPT file
• DISK: generates a report on file "IMPRPT.LST"

Details

FTI converts two-dimensional frequency domain data, usually created by FTF, to spatial domain imagery data using one of the following transformations: inverse Fourier with real and imaginary input (FIR); inverse Fourier with magnitude, phase input (FMP); inverse Walsh (WAL); inverse Hadamard (HAD); or inverse Cosine (COS).

For Fourier transformations (FIR or FMP), 32-bit floating point values must be provided on input, either in a single complex channel, or in two real-valued channels. If a complex channel is used for input, the format is reset to FIR (real and imaginary values). The zero frequency (DC component) must be in the center of the input image. For the COS, HAD and WAL inverse transformations, a single 32-bit real input channel is required and the zero frequency should be at the upper-left corner of the image. In all cases, the result is a single output channel. For the FIR and FMP transformations the output channel may be complex.

Before running FTI, ensure that the output file (FILO) exists; if it does not, create it by executing CIM.

The input window size (Xsize, Ysize) must be a power of 2 (for example: 64,128, 256, 512, ...). The output window size must not exceed the input window size.

If an input window is specified, the function removes all frequencies outside the defined window from the inverse transformation, effectively performing a frequency filtering operation. The input window must be carefully positioned to achieve the desired effect. In the most common applications, the high frequencies are eliminated; in these cases, the window should be centered within the image for the two Fourier transforms (FMP and FIR), and positioned in the upper-left corner of the image for the remaining transformations (WAL, HAD and COS).

The inverse transformation recreates the full extent of the original spatial image used to create the transformed image. The recreated spatial image is then placed in the area specified by the output window. If the window is defaulted to the full image area, the spatial extent and resolution of the recreated image are the same as that of the original spatial image. If a smaller output window is specified, the full extent of the recreated image is downsampled to fit the specified area. In this case, the function performs two functions: the frequency filtering and spatial downsampling.

Algorithm

Refer to the Algorithm section of the FTF help for algorithm descriptions.

References

Gonzalez, R.C. and Wintz, P. [1987]. Digital Image Processing. 2nd Edition, Addison-Wesley, Massachusetts.