Lecture Signals, systems & inference – Lecture 24: Matched filtering

The following will be discussed in this chapter: Matched filtering for detecting known signal in white Gaussian noise, matched filter performance, Q(.) function for area in Gaussian tail, matched filter properties, on-off signaling in noise, antipodal signaling,. | Lecture Signals, systems & inference – Lecture 24: Matched filtering Matched filtering , Spring 2018 Lec 24 1 Matched filtering for detecting known signal in white Gaussian noise r[n] g[n] g[0] ‘H1’ LTI, h[∙] Threshold g 7 6 n=0 ‘H0’ 2 Matched filter performance f(g|H0) f(g|H1) sU E g = a r[n]s[n] g E PM n PFA 3 Q(.) function for area in Gaussian tail The tail area to the right of x under a Gaussian PDF of mean 0 and standard deviation 1 is tabulated as the tail-probability function: Z 1 1 v 2 /2 Q(x) = p e dv 2⇡ x Useful bounds: 2 2 x e x /2 1 e x /2 2 p < Q(x) < p , x>0 (1 + x ) 2⇡ x 2⇡ For a Gaussian random variable of mean value ↵ and standard deviation , the area under the PDF to the right of some value is Z 1 ⇣ 1 (w ↵)2 /(2 2 ) ↵⌘ p e dw = Q 2⇡ 4 Matched filter properties •  Matched filter output in noise-free case (and before sampling) is the deterministic autocorrelation of the signal: g[n] = Rss [n] •  Matched filter frequency response magnitude accentuates frequencies where signal has strength relative to (spectrally flat) noise •  Matched filter frequency response phase cancels signal phase characteristic to allow all components to contribute at sampling time •  Matched filter maximizes “SNR” of sample fed to threshold test 5 On-off signaling in noise 1 0 1 0 0 1 1 0 1 1 0 0 1 d Gen. 2 0 -2 p(t) 0 200 400 600 800 1000 1200 2 1 0 -1 n(t) 0 200 400 600 800 1000 1200 10 0 -10 h(t) 0 200 400 600 800 1000 1200 2 0 -2 Dec. 0 200 400 600 800 1000 1200 1 0 1 1 0 6 1 1 0 0 1 0 0 1 Antipodal signaling 1 0 1 0 0 1 1 0 1 1 0 0 1 d Gen. 2 0 -2 p(t) 0 200 400 600 800 1000 1200 2 0 -2 n(t) 0 200 400 600 800 1000 1200 10 0 -10 h(t) 0 200 400 600 800 1000 1200 2 0 Dec. -2 0 200 400 600 800 1000 1200 1 0 1 0 0 7 1 1 0 1 1 0 0 1 Pulse compression for radar Read the simulation example .

Không thể tạo bản xem trước, hãy bấm tải xuống
TÀI LIỆU MỚI ĐĂNG
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.