Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution
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Answer to Problem 1E

  [2c12b2b12c]

Explanation of Solution

Given:

  [1,3,5,7]

Calculation:

Consider the given data

  x=[1357]

MCDT stands for Modified discrete cosine transform.

The MCDT of the matrix is y=Mx

  M=[ c c b b b b c c];whereb=cosπ8,c=cos3π8

  y=[ c c b b b b c c][ 1 3 5 7]     =[ 2c12b 2b12c]

Therefore, the MCDT of given input is

  [2c12b2b12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution
Check Mark

Answer to Problem 1E

  [c3bb3c]

Explanation of Solution

Given:

  [2,1,1,2]

Calculation:

Consider the given data

  x=[2112]

MCDT stands for Modified discrete cosine transform.

The MCDT of the matrix is y=Mx

  M=[ c c b b b b c c];whereb=cosπ8,c=cos3π8

  y=[ c c b b b b c c][ 2 1 1 2]     =[ c3b b3c]

Therefore, the MCDT of given input is

  [c3bb3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution
Check Mark

Answer to Problem 1E

  [8b+5c5b8c]

Explanation of Solution

Given:

  [4,1,3,5]

Calculation:

Consider the given data

  x=[4135]

MCDT stands for Modified discrete cosine transform.

The MCDT of the matrix is y=Mx

  M=[ c c b b b b c c];whereb=cosπ8,c=cos3π8

  y=[ c c b b b b c c][ 4 1 3 5]     =[ 8b+5c 5b8c]

Therefore, the MCDT of given input is

  [8b+5c5b8c]

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