NewQuiz2sol - 19 ECE 253a Digital Image Processing Pamela...

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# 19 ECE 253a Digital Image Processing Pamela Cosman 11/19/10 QUIZ 2 SOLUTIONS 1. Huffman Coding: (a) One possible codeword assignment is: Symbol Codeword Length Codeword A 2 11 B 2 10 C 2 01 D 3 001 E 4 0001 F 5 00001 G 5 00000 (Other correct answers are also acceptable.) (b) The expected length of this code is: E ( l ) = 0 . 3 × 2 + 0 . 26 × 2 + 0 . 2 × 2 + 0 . 1 × 3 + 0 . 05 × 4 + 0 . 05 × 5 + 0 . 04 × 5 = 2 . 47 bits c)GBCEDA is encoded to the sequence of 000001001000100111 d)If we flip the first bit of the sequence, we get 10,0001,001,0001,001,11 and is decoded to BEDEDA, and we see three symbol errors. Grading Criteria: 3 points for part (a), 1 point for each of the other parts. 2. Interpolation: h 3 (0) = 3 4 , and h 3 ( - 1) = h 3 (1) = 1 8 . The reconstructed function sampled at 0 is: f R (0) = 3 4 × f I (0) + 1 8 × f I ( - 1) + 1 8 × f I (1) which is not always equal to f I (0), so h 3 ( x ) is an approximator. 3. Median Filtering: (a) A line of width 1 running in any direction will be completely eliminated by the 3x3 square filter and by the sparse filter. It will be left untouched by the other filter. Consider now a
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