Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

MOOC | MOBILE | VIDEOS | BLOG | YOUTUBE | TWITTER | COMMENTS | ANALYTICS | ABOUT | CONTACT | COURSE WEBSITES | BOOKS | MATH FOR COLLEGE


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 = 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 = 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 2(-)which only need to compute are

2(4-7,12-15)

2(0-3,8-11)

2(0-7)

2(8-15)


Q5For N =24 =16, level L=3 and referring to referring to the figure 1 shown at this link, the only companion nodes associated with 3(0) and 3(1) are

3(4) and 3(5)

3(6) and 3(7)

3(14) and 3(15)

3(2) and 3(3)


Q6.  Given N = 4, and

.

 

 

 

 Corresponding to level L = 1, one can compute  3(2) as

-2 - 2i

4 - 6i

4 - 6i

-4 - 4i


Complete Solution

 

Multiple choice questions on other topics


AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS


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.

 

ANALYTICS