Re: Help Needed With Two Simple DSP-Related Questions

From: Lynn Kurtz (kurtzDELETE-THIS_at_asu.edu)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 00:46:29 GMT

On 20 Feb 2005 15:46:31 -0800, cpsmusic@yahoo.com (cps) wrote:

>Hi,
>
>Not sure if this forum is the right place for the following two
>questions--if not, let me know a more appropriate forum.
>
>I'm sitting in on a Signal Processing class which mainly involves the
>maths of Fourier analysis. My background is in music and it's a long
>time since I've done any maths. I'm not clear about two homework
>questions that have been given in the class.
>
>The first question is as follows:
>
>Is it true that any function x(t) can be written as the sum of an even
>part xe(t) and an odd part xo(t)? i.e. x(t) = xe(t) + xo(t)? If so,
>express xe(t) and xo(t) in terms of x(t).
>
>I assume that the first part of the question is true!
>
>x(t) = xe(t) + xo(t)
>

Hint: What happens if you but (- t) in the above equation?

>xe(t) = x(t) - xo(t)
>
>I'm not sure what to do to remove the xo term in this equation.
>
>The second question is:
>
>Find, using a general Taylor series expansion, all the solutions to
>the equation dy/dt = y.
>
>Does this mean that the derivative of y wrt t is y. In this case, all
>the derivatives of y will be y. This in turn means that when the
>Taylor series is expressed as a summation, y simply becomes a scaling
>factor. Is that correct?
>

Of course, y is a function of t and the taylor series is expanded
about some point a. So if you mean y(a), then, yes.

--Lynn

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