Frequency Estimation

Frequency Estimation Techniques Peter J. Kootsookos [email_address]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Talk Summary

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Some Acknowledgements

[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques What is frequency estimation?

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques What other problems are there?

[object Object],Frequency Estimation Techniques What other problems are there? [continued]

[object Object],Frequency Estimation Techniques What other problems are there? [continued] Thanks to Barry Quinn & Ted Hannan for the plot from their book “The Estimation & Tracking of Frequency”.

Frequency Estimation Techniques What other problems are there? [continued] ,[object Object],[object Object],[object Object],[object Object],p m=1

Frequency Estimation Techniques What other problems are there? [continued] ,[object Object],[object Object],[object Object],p m=1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques The Maximum Likelihood Approach

[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques The Maximum Likelihood Approach [continued]

Frequency Estimation Techniques The Maximum Likelihood Approach [continued] ,[object Object],[object Object],[object Object],t=0 T-1

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Subspace Techniques ^ ^ Note: If R yy is full rank, the P Bar is the same as the periodogram.

[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Subspace Techniques - Signal ^ ^ k=1 p k=1 p

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Subspace Techniques - Noise ^ ^ M k=p+1 While Pisarenko is not statistically efficient, it is very fast to calculate.

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Quinn-Fernandes

[object Object],Frequency Estimation Techniques Quinn-Fernandes [continued]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Associated Problems

[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Associated Problems: Analytic Signal Generation

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Associated Problems: Analytic Signal Generation [continued] Makes sure the DC term is correct.

[object Object],[object Object],[object Object],Frequency Estimation Techniques Associated Problems: Analytic Signal Generation [continued]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Kay’s Estimator and Related Estimators

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Frequency Estimation Techniques Kay’s Estimator and Related Estimators [continued] ^  T-2 t=0

[object Object],[object Object],[object Object],Frequency Estimation Techniques Kay’s Estimator and Related Estimators [continued]

[object Object],[object Object],Frequency Estimation Techniques Associated Problems: Cramer-Rao Lower Bound ^

[object Object],[object Object],[object Object],Frequency Estimation Techniques Associated Problems: Cramer-Rao Lower Bound [continued] ^  p m=1

Frequency Estimation Techniques Associated Problems: Threshold Performance Key idea: The performance degrades when peaks in the noise spectrum exceed the peak of the frequency component. Dotted lines in the figure show the probability of this occurring.

Frequency Estimation Techniques Associated Problems: Threshold Performance [continued] For the multi-harmonic case, two threshold mechanisms occur: the noise outlier case and rational harmonic locking. This means that, sometimes, ½, 1/3, 2/3, 2 or 3 times the true frequency is estimated.

[object Object],Frequency Estimation Techniques Thanks!

Frequency Estimation Techniques Good-bye!

Frequency Estimation

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