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8.3 MINIMUM VARIANCE SPECTRUM ESTIMATION

8.3 MINIMUM VARIANCE SPECTRUM ESTIMATION. STATISTICAL DIGITAL SIGNAL PROCESSING AND MODELING. Minimum Variance Spectrum Estimation. Develop the Minimum Variance (MV) method of spectrum estimation, which is an adaptation of the Maximum Likelihood Variance (MLM) developed by Capon.

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8.3 MINIMUM VARIANCE SPECTRUM ESTIMATION

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  1. 8.3 MINIMUM VARIANCESPECTRUM ESTIMATION STATISTICAL DIGITAL SIGNAL PROCESSING AND MODELING

  2. Minimum Variance Spectrum Estimation • Develop the Minimum Variance (MV) method of spectrum estimation, which is an adaptation of the Maximum Likelihood Variance (MLM) developed by Capon.

  3. Minimum Variance Spectrum Estimation

  4. Minimum Variance Spectrum Estimation • Design a bank of bandpass filter with center frequency so that each filter rejects the maximum amount of out-of-band power while passing the component at frequency with no distortion. • Filter with each filter in the filter bank and estimate the power in each output process . • Set equal to the power estimated in step (2) divided by the filter bandwidth.

  5. Minimum Variance Spectrum Estimation • To derive the minimum variance spectrum estimate, we begin with the design of the bandpass filter bank.

  6. Minimum Variance Spectrum Estimation

  7. Minimum Variance Spectrum Estimation • Estimate the power spectrum by dividing the power estimate by the bandwidth of the bandpass filter.

  8. Minimum Variance Spectrum Estimation

  9. Minimum Variance Spectrum Estimation

  10. Minimum Variance Spectrum Estimation • The larger the order of the filter the better the filter will be in rejecting out-of-band power.

  11. Minimum Variance Spectrum Estimation • Example 8.3.2 The MV Estimate of an AR(1) Process

  12. Minimum Variance Spectrum Estimation

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