Autocorrelation test When N is sufficiently large,the distribution of the estimated autocorrelation coefficients 6(/)=(/(0)is approximately Gaussian with zero mean and variance of 1/N. ·The approximate95 percent confidence limits are±l.96/√W. Any estimated values of (far beyond the confidence limits are viewed as "very"different from zero,thereby indicating nonwhiteness of the residual signal(残差信号)
• When N is sufficiently large, the distribution of the estimated autocorrelation coefficients is approximately Gaussian with zero mean and variance of 1/N. • The approximate 95 percent confidence limits are . Any estimated values of far beyond the confidence limits are viewed as “very” different from zero, thereby indicating nonwhiteness of the residual signal（残差信号）. Autocorrelation test ˆ( ) ( ) (0) l r l r = ˆ ˆ 1 96 N ˆ( )l
Power spectrum density test_ Given a set of data x(n,the standardized cumulative periodogram is defined by k<1 标准累积周期 立e) 图的定义 i(k) 1≤k≤K (8.1.4) k>K 利用标准累积周期图判定残差信号是否为白噪声信号，K=N2
Given a set of data the standardized cumulative periodogram is defined by 1 { ( )} 0 N x n n − = Power spectrum density test 标准累积周期 图的定义 利用标准累积周期图判定残差信号是否为白噪声信号, K=N/2
Power spectrum density test If the process x(n)is white Gaussian noise(WGN),then the random variables ()=1,2,.K,are independently and uniformly distributed in the interval(0,1),and the plot should be approximately linear with respect to k.The hypothesis is rejected at level 0.05 if (k)exits the boundaries specified by i(k) 7()=长±1.36(K-) 1≤k≤K K-1 (8.1.5)
If the process x(n) is white Gaussian noise (WGN), then the random variables are independently and uniformly distributed in the interval (0,1), and the plot should be approximately linear with respect to k. The hypothesis is rejected at level 0.05 if exits the boundaries specified by I k k K ( ) 1 2 = I k( ) Power spectrum density test I k( )
Partial autocorrelation test Introduction for partial autocorrelation sequence (PACS) r(0) r,(1) r (1) 1 r(1 r(0) r.(1-1) a,(1) .: r(1) r(1-1) rx(0) a,(1) 0 ()=k是PACS的第I个元素，同时也是格型结构的第级系数。但 是σ2是未知的？删去Y-W方程第一行，并变形 变形的Y-W方程 r(0) r.(1-1)] a,(1) r(1) : rx(1-1) r(0) a,(1) r,"(1)
Partial autocorrelation test Introduction for partial autocorrelation sequence (PACS) 变形的Y-W方程 al (l)=kl是PACS的第l个元素，同时也是格型结构的第l级系数。但 是 2 是未知的？删去Y-W方程第一行，并变形
Partial autocorrelation test Introduction for partial autocorrelation sequence(PACS) 在已知残差信号x()}的情况下，我们可以得到其自相关估计 .(m）=N氵 x(k+m)x'(k) 进而得到各阶数的估计自相关矩阵，并通过删去第一行的Ye- alker方程得到PACS中各元素{k。 F(0) 产(1-1) a,(1) -(1) (1-1) P(0) a,() -户x(I)
Partial autocorrelation test 在已知残差信号{x(n)}的情况下，我们可以得到其自相关估计 进而得到各阶数的估计自相关矩阵 ，并通过删去第一行的YuleWalker方程得到PACS中各元素{kl }。 ˆ R x Introduction for partial autocorrelation sequence (PACS)