Estimation of Sinusoids in White Noise

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Estimation of Sinusoids in White Noise

• Selami Ciftci

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Looking for Sinusoids

• Given N data points of a signal y(n)
• Find
• M, the number of sinusoids
• f, the frequencies
• A, the amplitudes
• s, the variance of the noise

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Our Good Old Friend DFT

• Is this the solution?
• Non-Parametric Approach
• Pluses?
• The estimated M, fs and As

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1,2 or more?

• Essential for MUSIC and ESPRIT
• MDL Algorithm

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Modified Covariance Method

• Higher spectral resolution than Yule-Walker
  Method
• Comparison with Burg algorithm
• Not having any line-splitting problems
• Less sensitivity to initial phase
• Noise variance is 0.6838

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Power Spectrum Estimate
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MUSIC

• An eigenspace method
• Based on a grid search
• Noise variance is 0.6879

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Power Spectrum Estimate
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ESPRIT

• An eigenspace method
• Noise variance is 0.6860

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Last Words

• MDL worked, how about AIC and their AR model
  versions
• Power computation
• Loading the data
• Computation time