211A_1_final2009

211A_1_final2009 - EE211A Fall Quarter, 2009 Digital Image...

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EE211A Digital Image Processing I Fall Quarter, 2009 1 Final Exam 1. 2D DFT (20 points) The above 256x256 image u ( m , n ) contains a periodic pattern of 64x64 squares of intensity 255 on a background of intensity 0. The center (not the upper left corner) of the above image is the (0, 0) location. The square centered at (0, 0) goes from 31 , 32 m n - . All the other squares are the same size and are centered at locations offset from the central square (both vertically and horizontally) by integer multiples of 128. Identify all the , k l locations where ( , ) v k l , the 2D DFT of u ( m , n ) will be nonzero.
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EE211A Digital Image Processing I Fall Quarter, 2009 2 2. Transforms ( 20 points) Consider a 1D transform defined as follows: v ( k ) = 1 N u ( n ) cos 2 π nk N + sin 2 nk N n = 0 N - 1 a) (5 points) In matrix notation, the transform can be described as v = A u where u is an N by 1 input vector, A is an N x N transform matrix, and v is an N by 1 output vector. Specify the elements of the matrix A for the N=4 case. b) (15 points)
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211A_1_final2009 - EE211A Fall Quarter, 2009 Digital Image...

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