It is known that the output of a distortionless linear system is given by y(t)-Ax(t-t), where...

 

Transcribed Image Text:

It is known that the output of a distortionless linear system is given by y(t)-Ax(t-t), where A is the gain of the system, t is the time delay, x(t) is the input. It is often convenient to evaluate the performance of a linear system by comparing the system output with an amplitude-scaled and time-delayed version of the input. The mean square error is then €² (A, T) = [y (t)- Ax (t - T)]² The values of A and t that minimize this expression, denoted Am and tm, respectively, are defined as the system gain and system delay. Show that, with these definitions, Rxy (Tm) Am = a. The system gain is R, (0) €2 (Am, Tm) R,(0) - = Ray (Tm) R, (0) b. And the resulting system mean-squared error is c. Also show that the signal power at the s R², (Tm) SD = A² R₂ (0) d. System output is R, (0) SD R², (Tm) = e. The output SNR ratio is No R. (0) R, (0)-R2, (Tm); Np is the mean-square error It is known that the output of a distortionless linear system is given by y(t)-Ax(t-t), where A is the gain of the system, t is the time delay, x(t) is the input. It is often convenient to evaluate the performance of a linear system by comparing the system output with an amplitude-scaled and time-delayed version of the input. The mean square error is then €² (A, T) = [y (t)- Ax (t - T)]² The values of A and t that minimize this expression, denoted Am and tm, respectively, are defined as the system gain and system delay. Show that, with these definitions, Rxy (Tm) Am = a. The system gain is R, (0) €2 (Am, Tm) R,(0) - = Ray (Tm) R, (0) b. And the resulting system mean-squared error is c. Also show that the signal power at the s R², (Tm) SD = A² R₂ (0) d. System output is R, (0) SD R², (Tm) = e. The output SNR ratio is No R. (0) R, (0)-R2, (Tm); Np is the mean-square error

Answer rating: 100% (QA)

ANSWERS a Rxy Tm R 0 a b Am Tm Ry0 Ry R 0 c e2 A T y 1 Ax 1r d y t Ax tt e S... View the full answer