PREP 2014 Question Authoring - Archived

problem testing function as user defined values

problem testing function as user defined values

by Joel Trussell -
Number of replies: 0
I am creating a problem with a symbolic answer. I thought the easy way to do this would be just to create my own function X(w) = w, and use it in the answer. The Fourier transform of x(n) + x(n-1) is X(w) + exp(-j*w)*X(w). It doesn't really matter what X(w) is as long as I can evaluate it. See the code below.

DOCUMENT();

# modified to use j for i = sqrt(-1)
$complexJ =1; # 0 => i, 1 => j
$I = ($complexJ)? 'j': 'i';

loadMacros(
"PGstandard.pl", # Standard macros for PG language
"MathObjects.pl",
($complexJ) ? "contextComplexJ.pl" : "",
#"source.pl", # allows code to be displayed on certain sites.
"PGcourse.pl", # Customization file for the course
"parserFunction.pl",
);

# DTFT of aperiodic series geometric series

TEXT(beginproblem());

# Show which answers are correct and which ones are incorrect
$showPartialCorrectAnswers = 1;

##############################################################
#
# Setup
#
#
Context("Complex");
Context()->variables->are(w=>'Real');
#Context()->variables->are(n=> 'Real',w=>'Real'); #Context()->variables->remove(z); # only variables should be n and w
parserFunction("X(w)" => "w");

$n0 = random(1,9,1); # delay of sequence
$c1 = random(1,9,1); # gain of x(n)
$c2 = random(1,9,1); # gain of x(n-$n0)

#$Xp = Formula("$c1*X(w) - $c2*e**((-1)*j*w$n0)*X(w)")->reduce->with(test_at => [[0,0],[0,1],[0,2],[0,3]]); # used with two variables n and w
$Xp = Formula("$c1*X(w) - $c2*e**((-1)*j*w$n0)*X(w)")->with(test_at => [[0],[1],[2],[3]]);

##############################################################
#
# Text
#
#

Context()->texStrings;
BEGIN_TEXT
This problem is related to 4.17a in the text.
$PAR
Let \( x(n) \) be an arbitrary signal, not necessarily real valued, with Discrete Fourier transform, \(X(\omega ) \),
$BR Express the Discrete Fourier transform of the following signal in terms of \(X(w) \),
$BR Use \(w \) for \(\omega\)(omega) to make typing easy.
\[
y(n) = $c1*x(n) - $c2*x(n-$n0),
\]
$PAR

$BR \(Y(\omega )= \) \{ $Xp ->ans_rule(40)\}

END_TEXT
Context()->normalStrings;

##############################################################
#
# Answers
#
#

ANS($Xp->cmp());

ENDDOCUMENT();