the best order 2 least squares approximation to the data using the basic function 1 a n d cos 2 π t

Question

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Answer 1

Question

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

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Answer 2

Question

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

Answer 6

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

Answer 7

Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Answer 8

a.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function

P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is P2(t)=0 .

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

Answer 13

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Answer 14

b.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are,

here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=cos2πt+sin2πt yields P2(t)=cos2πt .

Answer 15

b.

Expert Solution

Answer 16

b.

Expert Solution

Answer 17

Expert Solution

Answer 18

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

Answer 19

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Answer 20

c.

Expert Solution

Explanation of Solution

Given information:

The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Calculation:

As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

P4(t)=−cos4πt yields P2(t)=0 .

Answer 21

c.

Expert Solution

Answer 22

c.

Expert Solution

Answer 23

Expert Solution

Answer 24

Ch. 10.1 - Prob. 1E Ch. 10.1 - Find the DFT of the following vectors: (a) [...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.2 - Use the DFT and Corollary 10.8 to find the...Ch. 10.2 - Prob. 2E

the best order 2 least squares approximation to the data using the basic function 1 a n d cos 2 π t

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To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

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To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Explanation of Solution

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

Explanation of Solution

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