z plane design

i'm designing a simple filter and cannot expand my transfer function
properly to remove the j part

(z-cos@-jsin@)(z-j)

the last one i made was
(z-cos@-jsin@)(z-cos@+jsin@)

which i was able to expand using trigometric identities to get

z^2 -2zcos@ + 1

i've been reading Strouds  futher engineering mathematics all day but
cant find a solution
this is prob something really simple i'm just not getting but if
someone could help me out or point me in the right direction i'd really
appreciate it

thanks

student wrote:
> i'm designing a simple filter and cannot expand my transfer function
> properly to remove the j part
> 
> (z-cos@-jsin@)(z-j)
> 
> the last one i made was
> (z-cos@-jsin@)(z-cos@+jsin@)
> 
> which i was able to expand using trigometric identities to get
> 
> z^2 -2zcos@ + 1
> 
> i've been reading Strouds  futher engineering mathematics all day but
> cant find a solution
> this is prob something really simple i'm just not getting but if
> someone could help me out or point me in the right direction i'd really
> appreciate it
> 
> thanks
> 
You are correct in that you cannot remove the imaginary part of the 
first expression.

You can only reduce a product of complex polynomials to a purely real 
one if all complex roots have one and only one matching root which is 
the complex conjugate.  z = cos theta + j sin theta is the complex 
conjugate of z = cos theta - j sin theta, so your second expression reduces.

So the transfer function is suspect.  Either you cooked it up without 
being aware of the need for complex conjugate roots, or there is 
something that you aren't telling us.  Are you sure that you are not 
working with I-Q data expressed as complex, and are being assigned to 
make some filters that are asymmetrical around frequency = 0?

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

thanks,
i get it now i think, i know at least what i have to change so i can
remove the j part

do you know of anywhere on the internet or any books that deal with
this?
my entire grasp is of this seems quite suspect

student wrote:
> thanks,
> i get it now i think, i know at least what i have to change so i can
> remove the j part
> 
> do you know of anywhere on the internet or any books that deal with
> this?
> my entire grasp is of this seems quite suspect
> 
Any good book on signal processing.  "Signals and Systems" by Oppenheim, 
Wilsky & Young is what I see most often on folks' bookshelves (including 
my own) -- I don't know how it'd be without taking the 2nd-year EE 
course for which it is the text, but IIRC it should do.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com