`$f1 = $f2`

, where `$f1`

is the AR part and `$f2`

is the MA part. In DSP this is usually written
y(n) = a1*y(n-1) + ... aN*y(n-N) + b0*x(n) + ... + bM*x(n-M).In the vector context, x, y, z are standard variables. So I remove them, add the variable n, and define dummy functions

`x(n)`

, `y(n)`

. The problem is that the equation comes out`yn =`

and not `y(n) =`

, The `x(n)`

seems fine. I've tried various modifications with various errors, but nothing works. I can change `y(n)`

to `q(n)`

and that works, but I really need yno to agree with standard texts.
code below

DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGstandard.pl", # Standard macros for PG language "MathObjects.pl", "AnswerFormatHelp.pl", "parserFunction.pl", "PGcourse.pl", ); TEXT(&beginproblem); $showPartialCorrectAnswers = 1; Context("Vector"); Context()->variables->remove(x); # only variables should be n Context()->variables->add(n=> 'Real'); # how to remove y and z from Vector context? # Component values here parserFunction("q(n)" => "n"); # dummy function parserFunction("x(n)" => "n"); # dummy function $Na1 = random(3,6,1); do {$Nb1 = random(3,6,1);} until ($Nb1 != $Na1); $Nmax = 6; for ($k =1;$k <= $Nmax;$k++) {$a1[$k] =0}; for ($k =1;$k <= $Nmax;$k++) {$b1[$k] =0}; $a1[0] = non_zero_random(-9,9,1); # a0 for ($k =1;$k <= $Na1;$k++) {$a1[$k] = random(-5,5,1)}; $b1[0] = non_zero_random(-9,9,1); # b0 for ($k =1;$k <= $Nb1;$k++) {$b1[$k] = non_zero_random(-5,5,1)}; for ($k =1;$k <= $Nmax;$k++) {$a1ans[$k] =0}; for ($k =1;$k <= $Nmax;$k++) {$b1ans[$k] =0}; $a1ans[0] = 1; for ($k =1;$k <= $Na1;$k++) {$a1ans[$k] = -$a1[$k]/$a1[0]}; for ($k =0;$k <= $Nb1;$k++) {$b1ans[$k] = $b1[$k]/$a1[0]}; $f1 = Formula("$a1[0]*y(n) + $a1[1]*y(n-1) + $a1[2]*y(n-2) + $a1[3]*y(n-3) + $a1[4]*y(n-4) + $a1[5]*y(n-5) + $a1[6]*y(n-6) ")->reduce; $f2 = Formula("$b1[0]*x(n) + $b1[1]*x(n-1) + $b1[2]*x(n-2) + $b1[3]*x(n-3) + $b1[4]*x(n-4) + $b1[5]*x(n-5) + $b1[6]*x(n-6) ")->reduce; $Na2 = 1; $Nb2 = random(4,6,1); for ($k =1;$k <= $Nmax;$k++) {$a2[$k] =0}; for ($k =1;$k <= $Nmax;$k++) {$b2[$k] =0}; $b2[0] = non_zero_random(-9,9,1); # b0 for ($k =1;$k <= $Nb2;$k++) {$b2[$k] = random(-4,4,1)}; $Nmax = 6; $f3 = Formula("y(n)")->reduce; $f4 = Formula("$b2[0]*x(n) + $b2[1]*x(n-1) + $b2[2]*x(n-2) + $b2[3]*x(n-3) + $b2[4]*x(n-4) + $b2[5]*x(n-5) + $b2[6]*x(n-6) ")->reduce; $a2ans[0] = 1; for ($k =1;$k <= $Na1;$k++) {$a2ans[$k] = -$a2[$k]}; for ($k =0;$k <= $Nb1;$k++) {$b2ans[$k] = $b1[$k]}; Context()->texStrings; TEXT(EV2(<<EOT)); \{image("direct_form_2.jpg")\} $BR This Problem is related to Problem 2.46 in the text. $PAR The problem is to determine the coefficients for the Direct Form II (figure above). For this problem, we will assume the maximum delay is $Nmax. You will need to find all coefficients. There are likely to be several zero coefficients, if the orders of the AR and MA parts are not equal. $PAR Give the coefficients of Direct Form II for the difference equation , $PAR a) \( $f1 = \) $BR \($f2\) $PAR For the coefficients, enter as vectors, \( {\bf a} = <a_0, a_1, ..., a_6>\) $BR and \( {\bf b} = <b_0, b_1, ..., b_6>\) $BR Note that some of the coefficients may be zero$BR \({\bf a} =\) \{ans_rule(40)\} \{ AnswerFormatHelp("vectors") \} $BR \({\bf b} = \) \{ans_rule(40)\} \{ AnswerFormatHelp("vectors") \} $PAR b) \( $f3 = $f4\) $PAR For the coefficients, enter as vectors, \( {\bf a} = <a_0, a_1, ..., a_6>\) $BR and \( {\bf b} = <b_0, b_1, ..., b_6>\) $BR Note that some of the coefficients may be zero$BR \({\bf a} =\) \{ans_rule(40)\} \{ AnswerFormatHelp("vectors") \} $BR \({\bf b} = \) \{ans_rule(40)\} \{ AnswerFormatHelp("vectors") \} EOT ANS(Vector(@a1ans)->cmp()); ANS(Vector(@b1ans)->cmp()); ANS(Vector(@a2ans)->cmp()); ANS(Vector(@b2ans)->cmp()); SOLUTION(EV3(<<'END_SOLUTION')); $PAR $BBOLD SOLUTION $EBOLD $PAR tmp holder END_SOLUTION ENDDOCUMENT(); # This should be the last executable line in the problem.