Algorithms for Image Processing and Computer Vision by Parker J. R

Author:Parker, J. R.
Language: eng
Format: epub
Publisher: John Wiley & Sons
Published: 2010-11-18T16:00:00+00:00

Figure 7.2b shows the Fourier transform of the curve. Note that it has a single peak at the point w = 8, which happens to correspond to the frequency of the original sine curve: eight cycles per 1024 pixels, or one cycle in 128 pixels. Figure 7.2c and d show a pair of sine curves and their Fourier transform, which has two peaks (one per sine curve).

The Fourier transforms shown in Figure 7.2 were computed by the C procedure slow.c, which uses Equation 7.4 to do the calculation. This does work fine, but is very slow, and it would not likely be used in any real system. Because of the very useful nature of the Fourier transform, an enormous effort has been extended to make it computationally fast. The essential C code from slow.c is shown in Figure 7.3, this can be compared with the code for the fast Fourier transform (FFT), which will be discussed in the next section. The complex numbers are implemented as structures, each having a real and imaginary component.

Figure 7.3: Source code for the obvious implementation of the Fourier transform.

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