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Unformatted text preview: Lesson [13] Power Spectrum Challenge [12] Lesson [13] Nonparametric Power Spectrum Analysis: A Survey (You will not be examined on this material) Wednesday Exam #2 review Practice Exam online Lesson [13] Challenge [12] Goertzels Algorithm was presented in the context of filters and 2 nd order filters of the form: This filters is called a " resonator and is designed to respond to a sinusoidal input at the n th harmonic, [ ] ( 29 2 1 1 / 2 cos 2 1 1 + = z z N n z W z H n N n Lesson [13] Architecture (real coefficients) Should you be concerned about the filter being unstable (poles on unit circle)? 2 nd order section pole locations for N=12, n=2 case. y [k] k=N =X[0] y n [k] k=N =X[n] y [k] y n [k] 2 /122 /12 Lesson [13] For n=2, N=12, the filterstransfer function is: The filters poles are located at W 12 2 and a zero of placed at W 122 as shown. Your training to date should lead you to the conclusion that the filter is conditionally stable. Conventional wisdow would state that if a sinusoidal tone arrives at the 2 nd harmonic, your toast. [ ] ( 29 2 1 1 / 2 cos 2 1 1 + = z z N n z W z H n N n Lesson [13] Goetzels algorithm is a replacement to a DFT/FFT, each filter computing a harmonic defined by y n [k] k=N =X[n] for the n th harmonic. A system having n=2, N=12, is designed to take in N=12 samples and compute the 2 nd harmonic component using Y[n]=y n [k] k=N . Even if the input is located at the 2 nd harmonic, the output (produced by a finite sum) remains bounded. [ ] ( 29 2 1 1 / 2 cos 2 1 1 + = z z N n z W z H n N n Lesson [13] Power Spectrum (Survey) Power Spectral Analysis Survey Why is power spectral analysis useful? Characterizes as signal or system based on their frequency domain signature. Applicable to both deterministic and arbitrary signal cases with and without additive noise. Can be use to quantify SNRs. Lesson [13] Power Spectrum Electromyogram (EMG) measures the electrical activity of muscles....
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This note was uploaded on 01/26/2012 for the course ECON 101 taught by Professor Flah during the Spring '10 term at Punjab Engineering College.
 Spring '10
 Flah

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