The MCDT of the given input.

Question

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Answer 1

Question

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

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Answer 2

Question

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

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Answer 3

Question

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

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Answer 4

Question

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

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Answer 5

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

Answer 6

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

Answer 7

Chapter 11.4, Problem 1E

a)

To determine

To find: The MCDT of the given input.

Answer 8

a)

Expert Solution

Answer to Problem 1E

[−2c−12b2b−12c]

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

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] =[ −2c−12b 2b−12c]

Therefore, the MCDT of given input is

[−2c−12b2b−12c]

Answer 13

b)

To determine

To find: The MCDT of the given input.

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

Answer 14

b)

To determine

To find: The MCDT of the given input.

Answer 15

b)

Expert Solution

Answer to Problem 1E

[−c−3bb−3c]

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

[−2,−1,1,2]

Calculation:

Consider the given data

x=[−2−112]

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] =[ −c−3b b−3c]

Therefore, the MCDT of given input is

[−c−3bb−3c]

Answer 20

c)

To determine

To find: The MCDT of the given input

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

Answer 21

c)

To determine

To find: The MCDT of the given input

Answer 22

c)

Expert Solution

Answer to Problem 1E

[−8b+5c−5b−8c]

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

[4,−1,3,5]

Calculation:

Consider the given data

x=[4−135]

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 −5b−8c]

Therefore, the MCDT of given input is

[−8b+5c−5b−8c]

Answer 27

Ch. 11.1 - Use the 22 DCT matrix and Theorem 11.2 to find the...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - (a) Prove the trigonometric formula...Ch. 11.1 - Prob. 7E Ch. 11.1 - Plot the data from Exercise 3, along with the DCT...Ch. 11.1 - Plot the data along with the m=4,6, and 8 DCT...Ch. 11.1 - Plot the function f(t), the data points...

The MCDT of the given input.

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To find: The MCDT of the given input.

Answer to Problem 1E

Explanation of Solution

To find: The MCDT of the given input.

Answer to Problem 1E

Explanation of Solution

To find: The MCDT of the given input

Answer to Problem 1E

Explanation of Solution

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Chapter 11 Solutions