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Intro to Spectral Analysis and Matlab

Intro to Spectral Analysis and Matlab. Q: How Could you quantify how much lower the tone of a race car is after it passes you compared to as it is coming towards you? How would you set the experiment up?. Running the Experiment .

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Intro to Spectral Analysis and Matlab

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  1. Intro to Spectral Analysis and Matlab Q: How Could you quantify how much lower the tone of a race car is after it passes you compared to as it is coming towards you? How would you set the experiment up?

  2. Running the Experiment . Data is often recorded in the time domain. The stored dataset is called a timeseries. It is a set of time and amplitude pairs.

  3. Frequency Domain (Do a Fourier Transform on Timeseries) We have converted to the Frequency Domain. This dataset is called a Spectra. It is a set of frequency and Amplitude pairs.

  4. What’s the Frequency? What’s the Period? What will this look like in the Frequency Domain? Time Domain

  5. What’s the new (red) period? How Does its amplitude Compare to the 1 s signal?

  6. Power Spectral Densities Secondary Microseism (~8 s) Primary Microseism (~ 16 s)

  7. QSPA PSD PDF

  8. The Mysterious Case of HOWD

  9. Sampling Frequency • Digital signals aren’t continuous • Sampled at discrete times • How often to sample? • Big effect on data volume

  10. How many samples/second are needed?

  11. Are red points enough?

  12. Aliasing FFT will give wrong frequency

  13. Nyquist frequency1/2 sampling frequency

  14. Nyquist frequency • Can only accurately measure frequencies <1/2 of the sampling frequency • For example, if sampling frequency is 200 Hz, the highest theoretically measurable frequency is 100 Hz • How to deal with higher frequencies? • Filter before taking spectra

  15. Summary • Infinite sine wave is spike in frequency domain • Can create arbitrary seismogram by adding up enough sine waves of differing amplitude, frequency and phase • Both time and frequency domains are complete representations • Can transform back and forth – FFT and iFFT • Must be careful about aliasing • Always sample at least 2X highest frequency of interest

  16. To create arbitrary seismogram • Becomes integral in the limit • Fourier Transform • Computer: Fast Fourier Transform - FFT

  17. Exercise plots

  18. Sine_wave column 2

  19. Sine_wave column 2

  20. Sine_wave column 2 and 3

  21. Sine_wave column 2 and 3 sum

  22. Spectra, column 2

  23. Spectra, columns 2, 3

  24. Spectra, column 2, 3, 2 and 3 sum

  25. Multi_sine, individual columns

  26. Multi_sine, individual columns

  27. Multi_sine spectra

  28. Spike in time

  29. Spike in time, frequency

  30. Rock, sed, bog time series

  31. Rock spectra

  32. Rock (black), Sed (red), bog (blue)

  33. Spectral ratio sed/rock

  34. Basin Thickness • Sediment site • 110 m/s /2.5 Hz = 44 m wavelength • Basin thickness = 11 m • Peat Bog • 80 m/s /1 Hz = 80 m • Basin thickness = 20 m

  35. Station LKWY, Utah raw Filtered 2-19 Hz Filtered twice

  36. Station LKWY, Utah raw Filtered 2-19 Hz Filtered twice

  37. Zoomed in once

  38. Zoomed in once

  39. Zoomed in again

  40. Triggered earthquakes

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