Infinitesimal signal power Note that ()e (lvere DTT) Interpretation: ()E=(dw (w)dw =infinitesimal signal power in the band 2020-01-1
2020-01-18 11 Infinitesimal signal power
Second Definition of PSD (w)= N→∞ wf Note that (w)=lim N->o E{是(P where N Yw(w)=∑y(t)e-iwt t=1 is the finite DTFT of {y(t)). 2020-01-18 12
2020-01-18 12 Second Definition of PSD
后向共轭信号序列：功率谱 -i N-→0 lim E N-→0 lim E W-→0 2020-01-18 13
后向共轭信号/序列：功率谱 2020-01-18 13 2 1 2 * 1 2 1 * 1 ( ) lim ( ) 1 lim ( ) 1 lim ( ) N i t N t N i t N t i t N t N E y t e N E y t e N E y t e N
后向共轭信号/序列：幅度谱 yw-2⑩ 2元M - t=1 y(k)=∑y0e是 t=l =-W 2020-01-18 14
后向共轭信号/序列：幅度谱 2020-01-18 14 2 1 2 * * 1 1 2 * ( ) ( ) ( ) ( ) ( ) N i kt N t N i kt N t i kt N t N Y k y t e Y k y t e y t e
后向共轭信号/序列：AR模型参数 y(t)=ay(t-1)+ay(t-2)+...+any(t-n)+v(n) o) -de 62 lem-djei--d--d 2 adje-n--le a,y(t)=-a,-y(t-1)-ar-2y(t-2)-..-aiy(t-n+1)+x(t-n)+v(n) any'(t)=-an-iy'(t-1)-an-2y(t-2)--4y'(t-n+l)+y'(t-n)+v*(n) y(t-n)=ay(t-n+1)+..+a-2y(t-2)+ay(t-1)+ay(t)-v(n) 2020-01-18 15
2020-01-18 15 1 2 2 2 2 1 2 2 2 ( 1) ( 2) 1 2 2 2 * * * 2 * ( -1) 1 2 1 * * * * 1 2 1 ( ) ( 1) ( 2) ( ) ( ) ( ) 1 1 1 ( ) ( 1) ( 2) n v i i in n v in i n i n n v i i i n in n n n n n n y t a y t a y t a y t n v n a e a e a e e a e a e a a a e a e a e e a y t a y t a y t a y * * * * * * 1 2 1 * * * * * * 1 2 1 ( 1) ( ) ( ) ( ) ( 1) ( 2) ( 1) ( ) ( ) ( ) ( 1) ( 2) ( 1) ( ) ( ) n n n n n n t n y t n v n a y t a y t a y t a y t n y t n v n y t n a y t n a y t a y t a y t v n 后向共轭信号/序列：AR模型参数