s2004b - Equation Chapter 1 Section 1Spectral Estimation...

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Equation Chapter 1 Section 1Spectral Estimation Overview In this project you will explore and compare various parametric and non-parametric techniques for power density spectrum (PDS) estimation. The goal is to approximate the PDS with non-parametric direct methods, such as the periodogram, periodogram averaging, and the non-parametric indirect Blackman- Tukey method. You will also investigate parametric all-pole modeling for PDS estimation. In the process, you will have a chance to sort through many issues involving finite length signals and the DFT. Suggested Reading: Sections 10.6, 10.7, and 11.0 to 11.5. You are given a signal that is the result of passing white Gaussian noise with variance one () through a system. Figure 1: Generating The goal is to estimate the PDS of,. Recall that: Thus estimating is equivalent to estimating. Your goal is to construct estimates of from the samples of the colored noise. S2004b
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0 50 100 150 200 250 300 350 400 450 500 -5 0 5 n y[n] 0 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 |H(e j ϖ )| 2 Magnitude k The data for this project is contained in the file pj2data.mat . Copy this file into the local directory where you are working. This file contains two vectors. The vector y is a 512-point vector representing the discrete time signal. The vector Hejw2 is a 512-point DFT representing samples of the magnitude-squared response. It is the desired response that you are trying to estimate from. Hejw2 is given to you as a baseline for error calculation. You can load the data into your MATLAB environment using the load command. Just cd to the directory where you copied pj2data.mat and at the prompt type: load pj2data Your MATLAB environment will now have two vectors y and Hejw2 defined in it. Warning! If you had other variables named y and Hejw2 they will be overwritten by the load command. Figure 2: Plots of the data in pj2data.mat As a first exercise you may want to plot the data y and Hejw2 . They are plotted above for your convenience. Note that the k-indices on Hejw2 represent sampled values in the interval (i.e.).
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This note was uploaded on 01/16/2010 for the course ECE 4250 taught by Professor Hemami during the Fall '05 term at Cornell University (Engineering School).

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s2004b - Equation Chapter 1 Section 1Spectral Estimation...

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