Matched Filter (1) x[n] y[] h(n] T(x) What is the filter's impulse response,such that when sampled at NT is T(x) N-1 N-1 m= ∑x[hn-yN-1=∑z[h[N-1- k=0 k=0 N-1 T(2)=>x[k]s[k] k=0 whxiong@uestc.edu.cn 16
whxiong@uestc.edu.cn Matched Filter (1) 16 What is the filter’s impulse response, such that when sampled at NT is T(x) y[n] = N X¡1 k=0 x[k]h[n ¡ k] y[N ¡ 1] = N X¡1 k=0 x[k]h[N ¡ 1 ¡ k] T(x) = N X¡1 k=0 x[k]s[k]
Matched Filter (1) x[n] y[] h(n] T(x) What is the filter's impulse response,such that when sampled at NT is T(x) N-1 N-1 m= ∑xhn-内N-1-∑x[h[-1- k=0 k=0 N-1 T(2)=>x[k]s[k] hin =sN-1-n] Match Filter k=0 whxiong@uestc.edu.cn 17
whxiong@uestc.edu.cn Matched Filter (1) 17 What is the filter’s impulse response, such that when sampled at NT is T(x) y[n] = N X¡1 k=0 x[k]h[n ¡ k] y[N ¡ 1] = N X¡1 k=0 x[k]h[N ¡ 1 ¡ k] T(x) = N X¡1 k=0 x[k]s[k] h[n] = s[N ¡ 1 ¡ n] Match Filter
Matched Filter Matched Filter:Filter impulse response matched with the signal hin=sN-1-n] whxiong@uestc.edu.cn 18
whxiong@uestc.edu.cn Matched Filter 18 Matched Filter: Filter impulse response matched with the signal h[n] = s[N ¡ 1 ¡ n]
Matched Filter Matched Filter:Filter impulse response matched with the signal hin =s N-1-n] Match Filter Maximizes the SNR at the Output y whxiong@uestc.edu.cn 19
whxiong@uestc.edu.cn Matched Filter 19 Match Filter Maximizes the SNR at the Output y Matched Filter: Filter impulse response matched with the signal h[n] = s[N ¡ 1 ¡ n]
Matched Filter Matched Filter:Filter impulse response matched with the signal hin =s N-1-n] Match Filter Maximizes the SNR at the Output y Define:s=[s[0],s[1],..s[N-1]] h=[h[N-1],h[N-1],…h[01 whxiong@uestc.edu.cn 20
whxiong@uestc.edu.cn Matched Filter 20 h = [h[N ¡ 1];h[N ¡ 1]; ¢¢¢h[0]] T Match Filter Maximizes the SNR at the Output y Matched Filter: Filter impulse response matched with the signal h[n] = s[N ¡ 1 ¡ n] s = [s[0]; s[1]; ¢¢¢s[N ¡ 1]] T Define: