1 / 52

Randomly Modulated Periodic Signals

Randomly Modulated Periodic Signals. Melvin J. Hinich. Applied Research Laboratories University of Texas at Austin. hinich@austin.utexas.edu. http://web.austin.utexas.edu/hinich/. Rotating Cylinder Data. Cat Brain EEG Seizure. Daily Sunspots. Hourly Alberta Electricity Demand.

niyati
Download Presentation

Randomly Modulated Periodic Signals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Randomly Modulated Periodic Signals Melvin J. Hinich Applied Research Laboratories University of Texas at Austin hinich@austin.utexas.edu http://web.austin.utexas.edu/hinich/

  2. Rotating Cylinder Data

  3. Cat Brain EEG Seizure

  4. Daily Sunspots

  5. Hourly Alberta Electricity Demand

  6. Hourly Alberta Electricity Prices

  7. One Week of Yen/US $ Returns

  8. Canadian $/US $ Rates of Return

  9. Bassoon Note

  10. Flute Note

  11. Definition of a RMP A signal is called a randomly modulated periodicity with period T=Nd if it is of the form

  12. Random Modulations are jointly dependent random processes that satisfy two conditions: Periodic block stationarity

  13. Finite Dependence Condition needed to ensure that averaging over frames yields asymptotically gaussian estimates are independently distributed if

  14. Fourier Series for Components

  15. Signal Plus Noise The modulation is part of the signal It is not measurement noise

  16. Artificial Data Examples

  17. Five Standard Deviations

  18. Three Standard Deviations

  19. Two Standard Deviations

  20. One Standard Deviation

  21. No Correlation in the Modulation

  22. Block Data into Frames The data block is divided into M frames of length T T is chosen by the user to be the period of the periodic component The t-th observation in the mth frame is

  23. Signal Coherence Function

  24. Frame Rate Synchronization The frame length T is chosen by the user to be the hypothetical period of the randomly modulated periodic signal. If T is not an integer multiple of the true period then coherence is lost.

  25. Signal Coherence Spectrum The signal-to-noise ratio is

  26. Estimating Signal Coherence

  27. StatisticalMeasureof Modulation SNR

  28. Chi Squared Statistic

  29. Coherent Part of the Mean Frame

  30. Spectrum of the Variance Fourier Series Expansion

  31. Sunspot Spectra

  32. Power & Signal Coherence Spectra - Demand

  33. Power & Signal Coherence Spectra - Prices

  34. Yen/$ Spectrum & Coherencies

  35. Exchange Rates Data 25 exchange rate series sampled half-hourly for the whole of 1996 with weekends removed. The weekend period is from 23:00 GMT on Friday when North American financial centres close until 23:00 GMT on Sunday when Australasian markets open. The incorporation of such prices would lead to spurious zero returns and would potentially render trading strategies which recommended a buy or sell at this time to be nonsensical. Removal of these weekend observations leaves 12,575 observations for subsequent analysis.

  36. Summary Statistics

  37. Coherence Results I

  38. Coherence Results II

  39. Coherent Part of Yen/$ Mean Frame

  40. Descriptive Statistics of Canadian$/US$ Daily Data • Sample size = 7569 20.7 Years • Mean = 0.557E-04 Std Dev = 0.270E-02 • Skew = 0.933E-01 Kurtosis = 3.62 • Max value = 0.191E-01 Min value = -0.184E-01 • Frames = 40 Frame Length = 186.8 • Frequencies in band = 93 • Maximum coherence probability = 0.999999 • Coherence threshold = 0.35

  41. Canadian$/US$ Daily Data Spectra

  42. Waterfall Spectrogramsof RMP+Noise SNR = - 38 dB

  43. Sigcoh Probability Waterfall of RMP+Noise SNR = - 38 dB

  44. Waterfall Spectrogramsof RMP+Noise SNR = - 44 dB

  45. Sigcoh Probability Waterfall of RMP+Noise SNR = - 44 dB

  46. Winglet Vibration Data

  47. Winglet Spectrum & Coherencies

  48. Prewhitened Winglet Spectra

More Related