Assume that we have an image represents a sinusoidal variation orthogonal to the x-axis with amplitude of 10 and period of 1 cm, that repeats infinitely in all directions within the plane. Further assume an average intensity of 10.
a) Sketch the 2D Fourier Transform (magnitude only) of this image on the (u,v) plane in units of cycles per cm, using "x" to denote an impulse in the frequency domain. (Recall that the Fourier transform of sinusoid is an impulse in the frequency domain)
b) Sketch the projection of the image on the x-axis, graphing pixel intensity as a function of x. (note: since the image repeats infinitely, this should be the average pixel intensity along each projection)
c) Sketch the projection of the image on the y-axis, graphing pixel intensity as a function of y. (note: same as in B)
D) What frequency is (or frequencies are) present in the x projection?
E) What frequency is (or frequencies are) present in the y projection?
F) Describe how the answers to D and E are evident from the sketch in A.
Hints:
- for part a) determine the equation of the sinusoidal, transform it into fourier domain and then plot the u,v plot
- for part b and c) the projection is the average of all signals parallel to the axis from
-infinity to infinity along the perpendicular axis