linear MMSE estimation

hi all,
we observe a random WSS process X(t) and its derivative X'(t).
if the autocorrelation function of X is R(tau)=exp(-abs(tau)),
find A and B so that A*X(t)+B*X'(t) is the best estimate for
X(t+d)if the performance index is the expected mean square error,
which is to get minimized?


please note that since R(tau) isnt differentiable at t=0,
the cross-correlation functions of X(t) and X'(t) don't exist.
regards

rambiz@gmail.com writes:

> hi all,
> we observe a random WSS process X(t) and its derivative X'(t).
> if the autocorrelation function of X is R(tau)=exp(-abs(tau)),
> find A and B so that A*X(t)+B*X'(t) is the best estimate for
> X(t+d)if the performance index is the expected mean square error,
> which is to get minimized?
> 
> 
> please note that since R(tau) isnt differentiable at t=0,
> the cross-correlation functions of X(t) and X'(t) don't exist.
> regards

Would you like us to type the solution in here or would you prefer we
order the solutions manual and have it sent to your home?
-- 
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Randy Yates wrote:
> rambiz@gmail.com writes:
> 
> 
>>hi all,
>>we observe a random WSS process X(t) and its derivative X'(t).
>>if the autocorrelation function of X is R(tau)=exp(-abs(tau)),
>>find A and B so that A*X(t)+B*X'(t) is the best estimate for
>>X(t+d)if the performance index is the expected mean square error,
>>which is to get minimized?
>>
>>
>>please note that since R(tau) isnt differentiable at t=0,
>>the cross-correlation functions of X(t) and X'(t) don't exist.
>>regards
> 
> 
> Would you like us to type the solution in here or would you prefer we
> order the solutions manual and have it sent to your home?

Thank you Randy.  I was going to say something, but I couldn't come up 
with quite the right tone.

-- 

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