Consider a phantom image given by f(x, y) = cos(w (xy)) where w may assume three...

Transcribed Image Text:

Consider a phantom image given by f(x, y) = cos(w (x−y)) where w may assume three different values W₁ = 0, W₂ = 0.25μm-¹ and w3 = 1.25µm-¹. We decide to sample this phantom image with a stepsize T = T = 2πμm. (a) Show that this image is bandlimited and give its frequency support for the three different values of w. (b) For which values of w does it satisfy the condition of Shannon's sampling theorem? (c) Give the expression of the samples of the phantom image for the three different values of w. (d) Notice that, for two of the three possible values for w, the samples found in question item c) are identical. Why does this mean that the phantom image cannot be reconstructed from its samples for one of these values? Give an explanation using the previous question item b). Consider a phantom image given by f(x, y) = cos(w (x−y)) where w may assume three different values W₁ = 0, W₂ = 0.25μm-¹ and w3 = 1.25µm-¹. We decide to sample this phantom image with a stepsize T = T = 2πμm. (a) Show that this image is bandlimited and give its frequency support for the three different values of w. (b) For which values of w does it satisfy the condition of Shannon's sampling theorem? (c) Give the expression of the samples of the phantom image for the three different values of w. (d) Notice that, for two of the three possible values for w, the samples found in question item c) are identical. Why does this mean that the phantom image cannot be reconstructed from its samples for one of these values? Give an explanation using the previous question item b).

Answer rating: 100% (QA)

SOLUTION a To determine if the image is bandlimited we need to analyze the frequency content of the given image function Lets examine the expression fx y cosx y for the three different values of For 0 ... View the full answer