CH1 Introduction to ADSP:Theory, Algorithm and Application “I hear,I forget; I see,I remember; Ido,I understand.” A Chinese Philosopher
CH1 Introduction to ADSP: Theory, Algorithm and Application “ I hear，I forget； I see，I remember； I do，I understand.” A Chinese Philosopher
Contents o S1.Filters:devices of signal processing .Classic Filter Optimal Filter Adaptive Filter o S2.Adaptive filtering applications 0 S3.Stochastic processes Partial characteristic:Autocorrelation Matrix (ACM) ●PSD Linear parametric model o S4.Mean Square Information Space 2020-01-18 2
2020-01-18 2 Contents S1. Filters: devices of signal processing Classic Filter Optimal Filter Adaptive Filter S2. Adaptive filtering applications S3. Stochastic processes Partial characteristic: Autocorrelation Matrix (ACM) PSD Linear parametric model S4. Mean Square Information Space
S1.Filters:devices of signal processing o Application ● signal of interest can be discerned more effectively in the filter output o Reduce additive noise or interference o Reveal the useful information o Theory ● Deals with linear filters,where the filter output is a (possibly time- varying)linear function of the filter input. 2020-01-18 3
2020-01-18 3 S1. Filters: devices of signal processing Application signal of interest can be discerned more effectively in the filter output Reduce additive noise or interference Reveal the useful information Theory Deals with linear filters, where the filter output is a (possibly timevarying) linear function of the filter input
(1)Two distinct theoretical approaches o Classical approach Aimed at designing frequency-selective filters such as lowpass/bandpass/notch filters etc. Based on knowledge of the gross spectral contents of both the useful signal and the noise components. It is applicable mainly when the signal and noise occupy clearly different frequency bands. o Optimal filter design Based on optimization theory,where the filter is designed to be "best"(in some sense). 2020-01-18 4
2020-01-18 4 (1) Two distinct theoretical approaches Classical approach Aimed at designing frequency-selective filters such as lowpass/bandpass/notch filters etc. Based on knowledge of the gross spectral contents of both the useful signal and the noise components. It is applicable mainly when the signal and noise occupy clearly different frequency bands. Optimal filter design Based on optimization theory, where the filter is designed to be “best” (in some sense)
(2)Optimal filter o The signal and noise are viewed as stochastic processes CDF,PDF,Partial character ●Parametric Model o Statistical criterion Minimizes the effects of the noise at the filter output according to some statistical criterion. o Based on minimizing the mean-square value of the difference between the actual filter output and some desired output 2020-01-18 5
2020-01-18 5 (2) Optimal filter The signal and noise are viewed as stochastic processes CDF, PDF, Partial character Parametric Model Statistical criterion Minimizes the effects of the noise at the filter output according to some statistical criterion. Based on minimizing the mean-square value of the difference between the actual filter output and some desired output