Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.341:DISCRETE-TIME SIGNAL PROCESSING OpenCourse Ware 2006 Lecture 18 Periodogram Reading:Sections 10.6 and 10.7 in Oppenheim,Schafer Buck(OSB). We begin this lecture by introducing three common illusions in spectral analysis: THREE ILLUSIONS .If you can't see it,it's not there.(the picket fence effect) The more zero padding,the better the spectral resolution.(resolution vs.sampling, spectral smearing) For a random process,as the data record length-oo,the magnitude-squared of the DTFT converges to the power spectral density.(the periodogram) In the last lecture,we discussed the first and the second illusions.The picket fence effect re- sults from the spectral sampling imposed by the DFT and can be avoided using zero padding. However,zero padding does not improve the spectral resolution which depends on the shape and length of the window. In this lecture,we will see the third illusion which relates to spectral analysis of stochastic signals.For a deterministic signal,more data (i.e.longer window)results in better frequency resolution,but this does not hold for a stochastic signal. The power spectral density(PSD)of a random process is useful for the following purposes: 1.System Identification x(t) h(t) +y(t) Piy()=Pz()H(j)2 P4x(2)=Pxx(2)H(j2) From the PSDs of input and output,we can estimate the frequency response of the system. 1Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.341: Discrete-Time Signal Processing OpenCourseWare 2006 Lecture 18 Periodogram Reading: Sections 10.6 and 10.7 in Oppenheim, Schafer & Buck (OSB). We begin this lecture by introducing three common illusions in spectral analysis: THREE ILLUSIONS • If you can’t see it, it’s not there. (the picket fence effect) • The more zero padding, the better the spectral resolution. (resolution vs. sampling, spectral smearing) • For a random process, as the data record length → ∞, the magnitude-squared of the DTFT converges to the power spectral density. (the periodogram) In the last lecture, we discussed the first and the second illusions. The picket fence effect re￾sults from the spectral sampling imposed by the DFT and can be avoided using zero padding. However, zero padding does not improve the spectral resolution which depends on the shape and length of the window. In this lecture, we will see the third illusion which relates to spectral analysis of stochastic signals. For a deterministic signal, more data (i.e. longer window) results in better frequency resolution, but this does not hold for a stochastic signal. The power spectral density(PSD) of a random process is useful for the following purposes: 1. System Identification 2 - y(t) - Pyy(Ω) = Pxx(Ω) H(jΩ) x(t) h(t) | | Pyx(Ω) = Pxx(Ω)H(jΩ) From the PSDs of input and output, we can estimate the frequency response of the system. 1