Midterm-2008

# Midterm-2008 - Detection and Estimation Midterm 2008 1(35...

This preview shows pages 1–2. Sign up to view the full content.

Detection and Estimation Midterm, 2008 1. (35%) Assume we have observed N samples x[0], x[1], …, x[N-1], whose model is expressed as 1 - N ..., 1, , 0 ], [ ) 2 cos( ] [ 0 = + = n n w f n A n x π . ( Case 1 ) Assume the frequency f 0 is known, and the noise w[n] is white Gaussian with unknown variance σ 2 . In this case, we are interested in estimating the parameter vector θ 1 = [A, σ 2 ] T . (a) Find the Fisher information matrix I( θ 1 ) . (12 pts) (b) Assume A ˆ and 2 ˆ σ are unbiased estimators of A and σ 2 , respectively. Find the lower bounds for ) ˆ var( A and ) ˆ var( 2 . ( 8 p t s ) (c) Assume the signal noise ratio is defined as 2 2 ) 2 ( α A = and ˆ is an unbiased estimator of . Find the lower bound of ) ˆ var( . (5 pts) ( Case 2 ) Assume the amplitude A and the frequency f 0 are unknown. The noise w[n] is white Gaussian with known but varying variance var(w[n]) = σ n 2 . In this case, we are interested in estimating the parameter vector θ 2 = [A, f 0 ] T

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Midterm-2008 - Detection and Estimation Midterm 2008 1(35...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online