Forums

linear MMSE estimation

Started by Unknown January 6, 2005
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