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Sample text
R) with r = 0, r = I1t , r = 211t . 0 IU; R. (r =211t) =J.. 20) integration takes place all over the interval which corresponds to positive productions ;(t);(t+r), and in the second integral, all over the interval which corresponds to negative productions Taking approximation equalities ;(t) ;(t +r). 13) does not hold, there is also a chance to determine variance DE of noise ;(t). t. 24) determining the variance DE is reduced to subtracting from the sums of the mean values of production integrals get) g(t), To+{r=O), get) get + 211t) , which were integrated over the intervals To+(r = 211t) =0 get) get + 211t) at r integral ~(t) ~(t + I1t) of positive and r = 2M , the productions g(t)g(t) and twofold value of the production which were integrated on the intervals To+ (r = I1t) of o positive productions get) get + I1t) at r = I1t .
O 2. Calculate values of cross correlation functions R .. ('t') for all the values /11/ 'C for centered signals ;(t). ~(t) by Robust Methods for Determining Estimates 45 Jr)=- Jg{t)l1{t+r)dt. T 1 Ro T 0 /iT) 0 o A{r = 0) 3. Determine error value at time shift r = O· At 4. Determine the mean error value with time shift by r = o· At by (AA{r = 0)) = [l/T- (r ='0 )]A{r = 0). 5. Calculate robustness value A~ 0 xy shift r between ; (t) and (r) of estimates Ro (r) ry{t + r) 0 at different time /iT) by It~ (r)= [To+ (r)- T~{r )](AIt{r = 0)) .
Thus based on the above, the following procedure of determining ;(t) variance DE of noise for the case when correlation between useful ~(t) and ;(t) is unavailable can be proposed. Compute autocorrelation function value R, , (r) at r = 0 signal 1. by 11K f T Roo(r=O)=-1 g(t)g(t)dt. 11K T o 0 0 2. t : T 1 Roo (r = I1t )=g{t )g{t + I1t )dt . 11K T o 0 0 3. Compute autocorrelation function R, , (r) with time shift KK R, "(r = 211t) KII =- f T 1 T g{t )g{t + 2M )dt . 0 0 o 4. Compute variance DE of noise by r =211t : Robust Methods for Determining Estimates D€ =Roo (r =0) + Roo (r = 2i1t) KK 2R KK 0 0 KX 31 (r = i1t).