Composite Test-One-sided Test E.g.,Positive DC in WGN with known noise statistics Ho xIn]wln] A>0 H xIn]=A+wln] n=01..W-1 Apply NP rule P(x;A,H1) eXxp(-a∑(x[n-A)2 P(x;A,Ho) >Y exp(-2a∑x2[m) -2(-2A∑m+N4)>1n ↓4>0 ∑xm>清ny+ A → 2 NA 2 whxiong@uestc.edu.cn 6whxiong@uestc.edu.cn Composite Test—One-sided Test 6 H1 x[n] = A + w[n] E.g., Positive DC in WGN with known noise statistics H0 x[n] = w[n] n=0,1…N-1 Apply NP rule A>0 P(x; A; H1) P(x; A; H0) = exp (¡ 1 2¾2 P(x[n] ¡ A) 2 exp(¡ 1 2¾2 Px 2[n]) > ° ¡ 1 2¾2 ³ ¡2A Xx[n] + NA 2 ´ > ln° Xx[n] > ¾2 A ln °+ NA 2 2 A>0 x¹> ¾2 NA ln°+ A 2 = ° 0