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Re: [Phys-l] Convolution (was Sun's image ...)



Now hang on a darn' minute!
Every single one of your students has been convolving three and four term
polynomials since third grade, and then some!

Look at this polynomial a(x) = x^3 + 2x^2 + 3x + 4
and b(x) = x^3 + 3x^2 + x + 3

The convolution is 1 5 10 18 21 13 12


Now if I mention that your students typically use x = 10
And they express two polynomials such as....
a(x) = 10^3 + 2X 10^2 + 3X 10 + 4 as 1234
and
b(x) as 10^3 + 3 X 10^2 + 10 + 3 X 10^0 as 1313


They convolve these polynomials.

In other words, they not only derive the convolution of these two polynomials, but they THEN
carry values greater than the base to the next column:
so (from the lowest power)
12 = 2 carry 1
13 plus 1 = 14 = 4 carry 1
21 plus 1 = 22 = 2 carry 2
18 plus 2 = 20 = 0 carry 2
10 plus 2 = 12 = 2 carry 1
5 plus 1 = 6
1

They then write
1 6 2 0 2 4 2 = 1234 X 1313

:-)

Who knew?
Brian W


Anthony Lapinski wrote:
Interesting. Thanks! I know there are numerous applications, but this is
too advanced for my students in trying to explain the solar image.

Take two polynomial equations, say
x^3 +2x^2 + 3x + 4 and x^3 + 4x^2 + 9x + 16

Just as we can multiply two scalars 3 X 4 = 12,
we can multiply these two polynomial functions in a similar way.