Re: Newby Q: How to specify reals
- To: mathgroup at smc.vnet.net
- Subject: [mg110547] Re: Newby Q: How to specify reals
- From: DBird <dbird at ieee.org>
- Date: Fri, 25 Jun 2010 07:26:13 -0400 (EDT)
- References: <hvq549$1o$1@smc.vnet.net>
Thanks to all the replies to this query. The "general" problem I'm
working on is to find the group delay of a "filter" expression. Using
the ideas of the replies, the procedure that seems to work best for
complicated expressions is as follows w/o M responses:
Clear[T1, T2, C1, C2, R1, R2, w]
$Assumptions = {T1, T2, C1, C2, R1, R2, w} \[Element]
Reals && {T1 > 0, T2 > 0, C1 > 0, C2 > 0, R1 > 0, R2 > 0, w >= 0}
H=expr
Simplify[ComplexExpand[Im[H]]/
ComplexExpand[Re[H]]]
Ang = ArcTan[%]
GD = -Simplify[D[Ang, w]]
Thanks again for all the replies.
Dave
On Jun 22, 4:00 am, DBird <db... at ieee.org> wrote:
> Trying the following procedure:
>
> In[41]:= {T1, T2, C1, C2, R1, R2, w} \[Element] Reals
>
> Out[41]= (T1|T2|C1|C2|R1|R2|w)\[Element]\[DoubleStruckCapitalR]
>
> In[42]:= x = R1 + I 1/(w C1)
>
> Out[42]= R1+I/(C1 w)
>
> In[43]:= Im[x]
>
> Out[43]= Re(1/(C1 w))+Im(R1)
>
> Question is, how do I specify the list {T1,T2,...} such that Im[x]
> yield just R1.
>
> I usually find I am missing something dumb...
>
> Thanks,
>
> Dave