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日期:2021-02-04 11:44

Dalhousie University

Faculty of Computer Science

CSCI 3162: Digital Media — Assignment 2

Winter Term 2021

due Friday, February 12, 23:59 AST

1. Matlab / Lossless Compression: The main purpose of this exercise is for you to gain some experience

programming in Matlab. On Brightspace you will find code implementing Huffman trees for

lossless compression. Be sure to read the README.

1. Adapt the code to also generate Shannon-Fano trees.

2. Test your Shannon-Fano code on the simple example included with the code. Draw the ShannonFano

tree generated by your code.

3. Compute both a Huffman tree and a Shannon-Fano tree for the larger example included with the

code. Compute and compare the compression rates achieved by the two algorithms.

For this assignment, do not use any code you find on the web. In all of your code, avoid loops as

much as possible. Please submit your code as well as other information as requested. Marks will be

based on the quality of your code and correctness of your findings as well as on the presentation of

your results.

2. Complex Numbers: For discrete-time signals x(n) as given below, compute

X(k) =

N

X?1

n=0

x(n) e?j2πkn/N

for k = 0, . . . , N ? 1. Simplify the resulting expressions as much as possible.

1. x(n) = δ(n)

2. x(n) = δ(n ? n0)

3. x(n) = a

n

4. x(n) = (

1 if 0 ≤ n ≤ N/2 ? 1

0 otherwise

5. x(n) = e j2πk0n/N

6. x(n) = cos(2πk0n/N)

Note: Identify geometric series wherever possible. The Dirac delta function is defined as

δ(n) = (

1 if n = 0

0 otherwise.

Assume a ∈ R and n0, k0 ∈ {0, 1, . . . , N ? 1}.

Please submit a scan of your detailed calculations with intermediate steps.

1

Submission instructions: Please submit your solutions on Brightspace. Submit a single archive file

(e.g., .zip or .tar) with one folder per problem. Remember that:

? All work you submit must be your own.

? Any questions you may have should be brought up during class time or posted on the Brightspace

discussion board.

? You must not share your calculations or code with anyone.

? You must not make use of any code you find on the web.

2


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