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. Graduate students must do all assignments individually. Undergraduate students may collaborate in groups of 2 for assignments. Only one submission with both names should be turned in from a group.
2. Clearly label your answers, and please submit answers in the order assigned.
3. (repeated from course syllabus) Academic Honesty: Unless explicitly stated otherwise, students are not permitted to access or compare any homework, or program-project answers with those of any other student or group past or present, alive or dead, or any Internet web site prior to submitting the assignment. Comparing answers, or getting answers off the Internet before submitting one's work is considered cheating. If you do not have time to complete an assignment, it is better to submit partial solutions than to get answers from someone else. While it is obviously difficult to enforce this policy, students who do not follow this policy should be keenly aware that in this class, they a re cheating, and if caught, will be prosecuted according to University guidelines. This applies both to the student (or group) who gets answers and the student (or group) who gives answers.
4. (repeated from course syllabus)  Lateness Policy: Assignments are due at the beginning of class. Unexcused late assignments will be penalized up to 10% per school day (weekends do not count) up to a 2-day maximum penalty of 20%. Without prior discussion with the professor, assignments will not be accepted more than two school days late without a university approved excuse.