Tasks

1. (4 pts) Consider Sayood's Example 13.2.1.
• (submit) Repeat this example with an angle of 30 degrees.
• (submit) Compute the mean squared error introduced in the reconstructed values using 30 degrees, and compare it with the error in the book's example that used approx. 68 degrees (arc tan 2.5).
2. (2 pts) The book says the transformed values in Table 13.2 are "energy preserving". 
• (submit) Explain "energy-preserving".
• (submit) Verify Table 13.2 is energy-preserving.
3. (3 pts)  Chapter 13: Projects and Problems: 2
• See Section 13.4.2
4. (2 pts) Compute all coefficients of the 2X2 Discrete Cosine Transform (DCT) transform matrix
• See equation 13.43
• Solve completely and show all work.
5. (2 pts) Compute the coefficient C_3,3 of the 8X8 DCT transform matrix.   Solve completely and show all work.
6. (2 pts) Reproduce the computations needed to derive the value -102.43 in Table 13.6.  You need to fully solve the calculations.
7. (3 pts) Estimate how many multiplications and additions are performed for a DCT transform of a 4" X 6" color photograph
• Assume a resolution of 150 dpi (dots or pixels per inch)
• As an aside, most of today's digital cameras do these calculations AND JPEG's quantization calculations AND JPEG's entropy encoding in a matter of seconds!
• For this answer, you may use the calculation approach discussed in class, but note that in practice, more efficient calculation methods are used.
8. (2 pts) Encode the sequence "12 14 12 -35 -35 200" of JPEG DC values using difference encoding and Table 13.9.
• Note that Table 13.9 does not explain how the category is encoded.  Hence, your answer can be in pairs of "category bit-sequence" for each DC value.
• Assume an initial virtual DC value of 0
9. (2 pts) Encode only the AC components of the following transformed and quantized 8x8 matrix:
•   7   2   4 -11   0   0   0   0
•   0   0   0   0   0   0   0   0
•  -3 -42   0   0   0   0   0   0
•   0   0   0   0   0   0   0   0
•   0   0   0   0   0   0   0   0
•   0   0   0   0   0   0   0   0
•   0   0   0   0   0   0   0   0
•   0   0   0   0   0   0   0   0
10. (2 pts) Use Table 13.10 to decode the following AC components.  Show your answer as an 8x8 matrix of integers.
• 010011110011011010

Notes

1. Students may work individually or in groups of 2.   Students in different groups may NOT compare answers prior to submitting their work. See the syllabus for the full statement on the lateness and academic honesty policies.