Returns thefast Fourier transform (FFT) for the input variable.
The array for which the FFT or the reverse FFT is computed. The size of each dimension may be any positive integer value.direction
A signed scalar value that determines the direction of the transform, between the time (or spatial) domain and the frequency domain.
The fast Fourier transform of array. The Cooley-Tukey fast Fourier transform algorithm is used for calculating the FFT.
A scalar string indicating the type of interleaving of 2D input signals containing signal-interleaved signals; and 3D input arrays containing image-interleaved images, or a volume. Valid strings and the corresponding interleaving methods are:
'signal' The 2D input image array arrangement is (x, p) for p signal-interleaved signals of length x.
'image' The 3D image array arrangement is (x, y, p) for p image-interleaved images of x-by-y.
'volume' The input image array is treated as a single entity.
The Fourier transform of a scaled-time function is defined by:
where w relates to the frequency domain, and t relates to the time (space) domain.
The data type of array is converted to complex, with the real part described by array and the imaginary part set to 0, unless it is already complex. The output array will have the same number and size of dimensions as array.
TIP: For more efficient transforms, choose dimensions for array that are a power of 2.
CAUTION: Take care to avoid wrap-around artifacts when filtering and convolving in the frequency domain. In particular, make sure your images are properly windowed and sampled before applying the Fast Fourier Transform, or false and misleading values will result.
The FFT function is used to transform the image into the frequency domain. For the example shown in Figure 2-39, the following parameters are used:
fft_aerial = FFT(aerial_img, -1)
Figure 2-39 PV-WAVE makes it easy to generate the Fourier spectrum for any image. Note that the diagonal, vertical, and horizontal lines in the Fourier spectrum correspond to the roads in the original 512-by-512 image, but are perpendicular to them; this is because of the 90-degree phase shift that occurs when moving from the space domain to the frequency domain.
Figure 2-40 PV-WAVE makes it easy to generate the Fourier spectrum for any image. Note that the diagonal, vertical, and horizontal lines in the Fourier spectrum correspond to the roads in the original 512-by-512 image, but are perpendicular to them; this is because of the 90-degree phase shift that occurs when moving from the space domain to the frequency domain.
(fft_aerial) can be run through these other three functions as follows:
display = SHIFT(ALOG(ABS(fft_aerial)), 256, 256)
display, is the image displayed on the right in Figure 2-39.
For background information, see Frequency Domain Techniques in Chapter 6 of the PV-WAVE User's Guide.
