电子科技大学：《现代数字信号处理理论与算法 Modern theory and algorithm of digital signal processing》课程教学资源（课件讲稿）02 PSD Estimation

CH2 PSD Estimation “Spectral Estimation is···an Art” Petre Stoica

CH2 PSD Estimation “ Spectral Estimation is ···an Art ” Petre Stoica

Content o Introduction o Periodogram and correlogram o Nonparametric methods o Parametric methods for Rational spectra o Parametric methods for line spectra o Filter-bank approach o Spatial methods P.Stoica,R.Moses-Spectral Analysis of Signals,Prentice Hall,2005(ISBN:0-13-113956-8) o Petre Stoica,Uppsala University o Randolph L.Moses,Ohio State University 2020-01-18 2

2020-01-18 2 Content  Introduction  Periodogram and correlogram  Nonparametric methods  Parametric methods for Rational spectra  Parametric methods for line spectra  Filter-bank approach  Spatial methods  P. Stoica, R. Moses-Spectral Analysis of Signals, Prentice Hall, 2005 (ISBN: 0-13-113956-8)  Petre Stoica, Uppsala University  Randolph L. Moses, Ohio State University

S1.Introduction o Spectral Estimation Problem o Applications o Deterministic Signals o Random Signals Two definitions of PSD ●Two main approaches 2020-01-18 3

2020-01-18 3 S1. Introduction  Spectral Estimation Problem  Applications  Deterministic Signals  Random Signals  Two definitions of PSD  Two main approaches

(1)Spectral Estimation Problem o Given:A finite record of a signal. o Determine:The distribution of signal power over frequency. signal spectral density 0+△0 兀 t=1.2 .@angular frequency in radians/(sampling interval) f frequency in cycles/(sampling interval) 2020-01-18 4

2020-01-18 4 (1) Spectral Estimation Problem  Given: A finite record of a signal.  Determine: The distribution of signal power over frequency.  ω = angular frequency in radians/(sampling interval)  f = frequency in cycles/(sampling interval)

(2)Applications o Temporal Spectral Analysis ● Vibration monitoring and fault detection Hidden periodicity finding Speech processing and audio devices ● Medical diagnosis Seismology and ground movement study ● Control systems design 。Radar,Sonar 0 Spatial Spectral Analysis Source location using sensor arrays 2020-01-18 5

2020-01-18 5 (2) Applications  Temporal Spectral Analysis  Vibration monitoring and fault detection  Hidden periodicity finding  Speech processing and audio devices  Medical diagnosis  Seismology and ground movement study  Control systems design  Radar, Sonar  Spatial Spectral Analysis  Source location using sensor arrays  ……

(3)Deterministic Signals If: ∑1g(t)2<o∞ 0o Then: Y(w)=∑y(t)e-iwt t=-o∞ exists and is called the Discrete-Time Fourier Transform DTFT) 2020-01-18 6

2020-01-18 6 (3) Deterministic Signals

Energy Spectral Density O0 S(w)=∑p(k)eiwk k=-0∞ where p(k)=∑y(t)y*(t-k) t=-0 Parseval's Equality: 22-2 S(w)dw 2020-01-18 7

2020-01-18 7 Energy Spectral Density

(3)Random Signals Random Signal random signal probabilistic statements about future variations △M2 current observation time 2020-01-18 8

2020-01-18 8 (3) Random Signals

PSD power spectral density Here: 21(e)2=∞ t三-O∞ But: E{(t)12<∞ E{.}=Expectation over the ensemble of realizations (t)2=Average power in y(t) 2020-01-18 9

2020-01-18 9 PSD = power spectral density

First Definition of PSD (w)=∑r(k)e-iwk k=-0∞ where r(k)is the autocovariance sequence (ACS) r(k)=E{y(t)y*(t-k)} r(k)=r*(-k), r(0)≥r(k) 2020-01-18 10

2020-01-18 10 First Definition of PSD