Holistic Numerical Methods

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MULTIPLE CHOICE TEST

(All Tests)

FOURIER TRANSFORM PAIR: FREQUENCY AND TIME DOMAIN

(More on Fourier Transform Pair: Time and Frequency Domain)

FAST FOURIER TRANSFORMS

(More on Fast Fourier Transforms)
 

Pick the most appropriate answer.

Q1.  Given two complex numbers: C1=2-3i, and C2=1+4i.  The product P=C1*C2 can be computed as

2+5i

-10+5i

-14+5i

14+5i

Q2.  Given the complex number C1=3+4i.  In polar coordinates, the above complex number can be expressed as C1=Aeiθ , where A and θ  is called the amplitude and phase angle of C1, respectively. The amplitude A can be computed as

3

4

5

7

Q3.  Given the complex number C1=3+4i.  In polar coordinates, the above complex number can be expressed as C1=Aeiθ , where A and θ  is called the amplitude and phase angle of C1, respectively. The phase angle θ in radians can be computed as

0.6435

0.9273
 2.864
 5.454

Q4.  For the complex number C1=-3+4i, the phase angle θ  in radians can be computed as

0.6435

0.9273

1.206

2.2143

Q5.  Given the function

 The Fourier transform  which will transform the function from time domain to frequency domain can be computed as

δ(a+t)

e-i(2πf)a

1

δ(t-a)

Q6.  Given the function

.

 The inverse Fourier transform ƒnp(t) which will transform the function from frequency domain to time domain can be computed as

eit

e-it

δ(t-0)

e-i(2πf)t

 

Complete Solution


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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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