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Material Type: Quiz; Class: Digital Image Processing; Subject: Electrical & Computer Engr; University: Georgia Institute of Technology-Main Campus; Term: Fall 2003;
Typology: Quizzes
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Friday, September 26, 2003
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Problem Max Score 1 20 2 20 3 20 4 20 5 20 Total 100
Problem Q.1: The Peruvian blowfish, which lives in shallow water, can sense light intensities that fall in the range from 10 to 1000 (measured in arbitrary units). Over this range the threshold for the fish’s ability to distinguish between two different light intensities, I and I +∆I, satisfies Weber’s Law with ∆I I
How many gray levels can the blowfish distinguish?
Problem Q2.3: Each of the items in Column A represents a symmetry condition on the impulse response of a 2-D digital filter. The items in Column B represent implied conditions in the frequency domain (plus a few additional equations whose intent, frankly, is to deceive). For each item in Column A, find an implied condition in Column B. Do not assume that h[n 1 , n 2 ] is real.
Column A Column B (i) h[n 1 , n 2 ] = −h∗[n 1 , n 2 ] (a) H(ω 1 , ω 2 ) = H(−ω 2 , ω 1 ) (ii) h[n 1 , n 2 ] = −h[n 2 , n 1 ] (b) H(ω 1 , ω 2 ) = H∗(ω 1 , ω 2 ) (iii) h[n 1 , n 2 ] = h[−n 2 , n 1 ] (c) e{H(ω 1 , ω 2 )} = 0 (iv) h[n 1 , n 2 ] = h[5 − n 1 , 5 + n 2 ] (d) H(ω 1 , ω 2 ) = −H(ω 2 , ω 1 ) (v) h[n 1 , n 2 ] = −h∗[−n 1 , −n 2 ] (e) m{H(ω 1 , ω 2 )} = 0 (f) H(ω 1 , ω 2 ) = −H∗(−ω 1 , −ω 2 ) (g) H(ω 1 , ω 2 ) = e−j5(ω^1 −ω^2 )H(−ω 1 , ω 2 ) (h) H(ω 1 , ω 2 ) = ej5(ω^1 −ω^2 )H∗(ω 1 , ω 2 ) (i) H(ω 1 , ω 2 ) = H∗(ω 2 , ω 1 ) (j) H(ω 1 , ω 2 ) = H(ω 2 , −ω 1 )
Problem Q2.4: Let x(t 1 , t 2 ) be a continuous image with Fourier transform X(Ω 1 , Ω 2 ) given in the figure below. The shaded region denotes a value of 1; the unshaded regions have a value of zero. The image is sampled in t 1 and t 2 with an ideal sampling system, resulting in a digital image x[n 1 , n 2 ].
2 π 4 π 6 π radians/second
2 π
4 π
6 π
(a) Determine the minimum sampling rates 1/T 1 and 1/T 2 such that x[n 1 , n 2 ] = x(n 1 T 1 , n 2 T 2 ) will represent x(t 1 , t 2 ) without aliasing. (b) Is your answer unique? (c) Assume that 1/T 1 = 1/T 2 = 3 samples/sec. Will x[n 1 , n 2 ] be purely real, purely imaginary, or complex? (d) Assume that 1/T 1 = 1/T 2 = 3 samples/sec. Is x[n 1 , n 2 ] separable?
