By Professor Dr. Heinrich Niemann (auth.)
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28) 1l = P(~) is a random variable with uniform distribution. 7. It works well if In eel, but there are problems if In = l. 32]. 33]. In the case of color and multispectral images additional techniques to normalize "gray" levels of spectral channels are used. 29) 33 P(x} _________________ t --------------! 7. An almost uniform distribution is obtained by dividing the y axis into Ln equal intervals and mapping them back to the x axis via the distribution y =P(x). The number of intervals of the x axis mapped to one interval of the y axis thus depends on P(x) This normalization yields chromaticities rand g, which are "true" colors and independent of intensity changes, and a luminance y, which depends on total intensity.
The resulting discrete sequence f is supposed to be repeated with period xo ' YO. The sequence is uniquely determined by the sampling interval, the period, and the sampling values f jk • The following result states that the spectrum of such a sequence is also a periodic sequence of coefficients Fuv. 9 that aliasing occurs if periodic repetitions overlap. 8: If fjk' j,k = 0,1, ••• , M-1 is a periodic sequence of sample values spaced at ~x, ~y and having period xo ' yo' then the spectrum is a periodic sequence of values FU,v ,spaced at sO' nO' having period ~s, ~n.
48]. The importance of FT and FFT for linear systems rests on the fact that system output may be computed efficiently via FFT by use of the following result which is given for a function of one variable. 87-121]). 66) is advantageous if the impulse response gj is nonzero in a sufficiently large number of points. This short account of linear systems is to give only the main ideas. Many additional results are contained in the above references. A system acting in the way described above on an input signal is also called a linear filter or, for short, a filter.