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Lesson 13 - Spectral_Estimation

# Lesson 13 - Spectral_Estimation - Power Spectrum...

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Lesson [13] Power Spectrum Challenge [12] Lesson [13] – Non-parametric Power Spectrum Analysis: A Survey (You will not be examined on this material) Wednesday – Exam #2 review Practice Exam on-line

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Lesson [13] Challenge [12] Goertzel’s 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 π
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 0 [k]| k=N =X[0] y n [k]| k=N =X[n] y 0 [k] y n [k] 2 π /12 -2 π /12

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Lesson [13] For n=2, N=12, the filter’stransfer function is: The filter’s poles are located at W 12 ± 2 and a zero of placed at W 12 -2 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 π
Lesson [13] Goetzel’s 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 π

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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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Lesson 13 - Spectral_Estimation - Power Spectrum...

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