Fourier Transforms and Complex Arithmetic

VISTA provides a limited capability for doing Fourier operations on images. VISTA internally can have "Fourier images" which have 2 pixels associated with each grid location, one for the real and one for the imaginary part. For the VISTA Fourier routines, the data in the spatial domain IS ASSUMED TO BE REAL. This assumption allows data in the frequency domain to be stored in almost the same size image as the spatial domain data. Because the Fourier transform of a real function is hermitian (symmetric real part and antisymmetric imaginary part), only the Fourier amplitudes of non-negative frequencies are stored to minimize redundancy and space. The Fourier-transformed image has the same size as the input image (except padded up to a power of 2), plus 2 extra columns, one each for the real and imaginary parts of the Nyquist frequency.

The VISTA Fourier Transform and Complex Arithmetic commands are:

The command FFT can be used to generate the direct fourier transform of a real image, the result is a complex image. IFFT would do the inverse fourier transform from a complex image into a real image. Both transformations can be perform in one or two dimensions. Command POWERS can be used after FFT to generate the periodogram estimation of the power spectrum.