Cap-Offset Block Filter Returns A Fractional Derivative Of O

[Bret Cahill]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=fracdiff

See the part on the fractional derivative of a constant.

This confirms that the cap filter is outputing something proportional
to a fractional derivative with an order between 0 and 1.

A big cap is near 0 and a small cap is near 1.

There is no integration step. It's a one step process after all.


Bret Cahill

 

[George Herold]

On Feb 11, 7:11 pm, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=fracdiff

See the part on the fractional derivative of a constant.

This confirms that the cap filter is outputing something proportional
to a fractional derivative with an order between 0 and 1.

A big cap is near 0 and a small cap is near 1.

There is no integration step.  It's a one step process after all.

Bret Cahill

If you are trying to do electronics I suggest you get some real
capacitors and see how they behave. A signal genernator, some C's,
R's and L's, a 'scope. You could really learn something.

George H.

 

[Susan Foreskineater]

Cap-Offset Block Filter Returns A Fractional Derivative Of Order 0 < nu < 1?

Blither-Cahill pounds keyboard imbecile factoid word arrangement syndrome
fail 'tard!

 

[Bret Cahill]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=fracdiff

See the part on the fractional derivative of a constant.

This confirms that the cap filter is outputing something proportional
to a fractional derivative with an order between 0 and 1.

A big cap is near 0 and a small cap is near 1.

There is no integration step.  It's a one step process after all.

Bret Cahill

If you are trying to do electronics I suggest you get some real
capacitors and see how they behave.  A signal genernator, some C's,
R's and L's, a 'scope.

Things will definitely get a little messier using real components but
the point here is even using ideal caps you aren't getting the
original signal back. What you get is a fractional derivative of
order nu close to zero which is close to the original signal (minus
offset, of course).

Same with inductors except nu is between 0 and -1.

What's interesting is that fractional derivatives are as difficult to
take as either integer or fractional integrals which makes sense since
integration and differentiation are considered the same operation here
except for the sign of nu.

As noted on a math site, the only reason taking counting number
derivatives is easy is because a lot of terms just happen to drop out.

Fractional derivatives need to be mentioned in undergraduate calculus
courses because counting number derivatives are deceptively easy.

I first thought about fractional derivatives playing around with caps
on SPICE. I didn't know it dated back to Leibniz but I was 100%% sure
I wasn't the first.

Ain't no low hanging fruit on Math Tree. Them mathematicians done
stripped Math Tree of bark, branches, roots . . .


Bret Cahill