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Thread Subject:
polynomial division

Subject: polynomial division

From: Elnaz

Date: 9 Nov, 2012 00:34:20

Message: 1 of 4

Could someone shed some light on why the final conditions of the filter delays provided by "filter" command is the remainder of the polynomial division r/g:
[q,remainder] = filter([zeros(1,n-k) 1],g,r);

Thanks,
Elnaz

Subject: polynomial division

From: Elnaz

Date: 9 Nov, 2012 05:38:13

Message: 2 of 4

Let me ask again:

I know that we can use"filter" command to implement polynomial division. For example if we want to divide r(x) by g(x) where r and g are polynomials of degree dr and dg respectively, one way to do it is:
[q,remainder] = filter([zeros(1,dg) 1],g,r);

I do understand how the quotient is calculated; but I do not understand how the remainder is been given here.

Thanks,
Elnaz

Subject: polynomial division

From: Bruno Luong

Date: 9 Nov, 2012 07:02:06

Message: 3 of 4

"Elnaz " <ebsadeghian@gmail.com> wrote in message <k7i4s4$6pn$1@newscl01ah.mathworks.com>...

>
> I do understand how the quotient is calculated; but I do not understand how the remainder is been given here.
>

A divided by B has quotient Q.

A ~ B*Q.

The remainder is R = A-B*Q, such that deg(R) < deg(B).

http://en.wikipedia.org/wiki/Polynomial_long_division

Bruno

Subject: polynomial division

From: Elnaz

Date: 9 Nov, 2012 15:53:15

Message: 4 of 4

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <k7i9pe$m5l$1@newscl01ah.mathworks.com>...
> "Elnaz " <ebsadeghian@gmail.com> wrote in message <k7i4s4$6pn$1@newscl01ah.mathworks.com>...
>
> >
> > I do understand how the quotient is calculated; but I do not understand how the remainder is been given here.
> >
>
> A divided by B has quotient Q.
>
> A ~ B*Q.
>
> The remainder is R = A-B*Q, such that deg(R) < deg(B).
>
> http://en.wikipedia.org/wiki/Polynomial_long_division
>
> Bruno

My question was/is that how the final states of filter delay tabs give the remainder?
The second output of the filter command gives the final states of filter delays. I want to understand how that can be equal to the remainder of polynomial division.

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