DESCRIPTIONComputes the real forward FFT of an image using a mixed-radix FFT. Images whose dimensions are multiples of 2, 3, 4, 5, and 7 are transformed more rapidly, but any shape image is acceptable. The output of the module is suitable for input to other Fourier*Img modules, or to the InverseFFTImg module. The output image is scaled by a constant factor so that ForwardFFTImg and InverseFFTImg provide an identity transformation up to floating point precision. The complex frequency domain output is stored in a packed format that occupies the same amount of storage as the input array. The format of the packed array is given below so that users may write their own modules to operate on the transformed data. The Fourier transformation is discussed in:
Digital Image Processing, Gonzales, R.C., Wintz, P., Addison Wesley, Second Edition, 1987, pp 100--109.
The Fourier Transform and Its Applications, Bracewell, R.N., McGraw-Hill, Second Edition, 1978.
Port: Img In
Spatial domain image.
Port: Img Out
Frequency domain image.
KNOWN PROBLEMSPACKED STORAGE FORMAT
The packed format for a column places the real part of the DC component at the beginning of a vector, omits the zero imaginary part, then lists the complex frequencies up to the Nyquist frequency, then places the real part of the Nyquist frequency, omitting the zero imaginary part. The columns are arrange the same way, with a DC column followed by real-imaginary pairs of columns out to the Nyquist frequency, which has only a single column. The Nyquist row (column) is omitted in the case of an odd number of columns (rows).
For an even number of columns (nc) and even number of rows (nr), the packed format is (R=real, I=imag):
DC Nyquist R R I R I ... R I R R R I R I ... R I R I R I R I ... R I I R R I R I ... R I R I R I R I ... R I I ................... R R I R I ... R I R I R I R I ... R I I R R I R I ... R I R Nyquist
© The Numerical Algorithms Group Ltd, Oxford UK. 2000