ldeal case E,o=2元 (S)WB(w-s)ds Ideally:WB(w)=Dirac impulse 6(w). 2020-01-18 26
2020-01-18 26 Ideal case
Practical case WB(w)/WB(0),for N=25 -10 2 -20 sin(2 Wg(@)= 9-30 Sins) -40 50 -60 -3 -2 0 2 ANGULAR FREQUENCY 2020-0: Main lobe 3dB width1/N. 27
2020-01-18 27 Practical case 2 sin( ) 2 ( ) sin( ) 2 B N W
Smearing effect o Main-Lobe Width:smearing or smoothing Φ(0) 6(o) smearing <1/N Periodogram resolution limit 1/N. 2020-01-18 28
2020-01-18 28 Smearing effect Main-Lobe Width: smearing or smoothing
Leakage effect o s Sidelobe Level:leakage (0)=δ(0) 6(o=(o) leakage /V 0 2020-01-18 29
2020-01-18 29 Leakage effect Sidelobe Level: leakage
Bias Properties For "small"N,severe bias ●AsN→o,WB(w)→6(w), so (w)is asymptotically unbiased. 2020-01-18 30
2020-01-18 30 Bias Properties