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Unformatted text preview: EEL 6502 Project #2 Due April 22, 2011 Description: The goal of this project is to design a real time principal component analyzer for music. Normally we use an FFT to find the frequency content of signals, but we can instead just create a bank of bandpass filters where the center frequencies are automatically placed at the points of the highest energies in the signal spectrum. This is exactly what a principal component analyzer does. The data provided for this project is a short violin clip (wave file, sampled at 44.1 KHz). The goal is to design a bank of filters that will represent the most energy contained in the sound. The network will be a multiple input multiple output system. The number of inputs is a tap delay line that defines a window of data where the period of the first principal component (the fundamental of the sound) exists. The number of outputs is going to be related to the number of principal components we decide to estimate (and must be smaller than the input window). Since you have the data set, you should estimate the appropriate number of inputs (the window size). The filters will be FIR filters, sharing the same tap delay line of the input window. Their parameters will be estimated with Sanger’s rule as we covered in class or the fixed point iterative algorithm that we called the CNEL rule (see slides). Your report should be in the format of an IEEE Paper (7 pages, double column). You should address the following points in your experimental investigation: 1
Start with a two output filter. The size of the filter’s delay line should be determined from the data. Are the frequency responses of these filters the same or different? Explain relating this with the FFT. How would you estimate the largest eigenvalue? How do you estimate the eigenvector? Please plot also the learning curve for both adaptation methods (eigenvalue across iterations), as well as weight tracks. State how the learning rate for the Sanger rule is selected. 2
Then use a number of outputs that will represent the 4 first eigenvectors. Show the evolution of all the eigenvalues across iterations in the same plot to show that the adaptation is sequential (a deflation). Once the filters converge, freeze the weights and reconstruct the input back from the sum of filter outputs and estimate the reconstruction error. Do a SVD on the input data and show that the values of the eigenvalues and eigenvectors estimated by this method approach the numerical solution. Estimate also the filters frequency response. 3
One of the difficulties is that the tap delay line size is rather large. Use a gamma delay line to decrease the number of taps to 20. Compare the performance (eigenvalue estimates, reconstruction error, convergence time) with #2. How would you relate the eigenvectors estimated with the gamma filter with the ones from #2? ...
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This note was uploaded on 06/05/2011 for the course EEL 6502 taught by Professor Principe during the Spring '08 term at University of Florida.
 Spring '08
 PRINCIPE
 Frequency

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