Holistic Numerical Methods

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MULTIPLE CHOICE TEST

(All Tests)

INFORMAL DEVELOPMENT OF FAST FOURIER TRANSFORM

(More on Informal Development of Fast Fourier Transform)

FAST FOURIER TRANSFORMS

(More on Fast Fourier Transforms)
 

Pick the most appropriate answer.

Q1.  Using the definition W=e-i(2π/N) , and the Euler identity e±iθ = cos(θ) ± i sin(θ), the value of W(N/6)  can be computed as

0.866 - 0.5i

-0.866 + 0.5i

-0.5 - 0.866i

0.5 - 0.866i

Q2.  Using the definition W=e-i(2π/N), and the Euler identity e±iθ = cos(θ) ± i sin(θ), the value of W(6N)  can be computed as

1 + i

1 - i

1

-1

Q3. Given N=2, and

.

 The first part of  can be expressed as

 

The values for can be computed as

Q4.  For N =24 =16, level L=2 and referring to the figure 1 shown at this link, the only terms of vector ƒ2(-)which only need to compute are

ƒ2(4-7,12-15)

ƒ2(0-3,8-11)

ƒ2(0-7)

ƒ2(8-15)

Q5. For N =24 =16, level L=3 and referring to referring to the figure 1 shown at this link, the only companion nodes associated with ƒ3(0) and ƒ3(1) are

ƒ3(4) and ƒ3(5)

ƒ3(6) and ƒ3(7)

ƒ3(14) and ƒ3(15)

ƒ3(2) and ƒ3(3)

Q6.  Given N = 4, and

.

 

 

 

 Corresponding to level L = 1, one can compute  ƒ3(2) as

-2 - 2i

4 - 6i

4 - 6i

-4 - 4i

Complete Solution

 

Multiple choice questions on other topics

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

  

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