intro to spectral analysis and matlab
DESCRIPTION
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 . - PowerPoint PPT PresentationTRANSCRIPT
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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?
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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.
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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.
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Time Domain
What’s the Frequency?What’s the Period?What will this look like in the Frequency Domain?
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What’s the new (red) period?How Does its amplitude Compare to the 1 s signal?
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Power Spectral Densities
Secondary Microseism (~8 s)
Primary Microseism (~ 16 s)
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QSPA PSD PDF
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The Mysterious Case of HOWD
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Sampling Frequency
• Digital signals aren’t continuous– Sampled at discrete times
• How often to sample?– Big effect on data volume
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How many samples/second are needed?
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Are red points enough?
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AliasingFFT will give wrong frequency
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Nyquist frequency1/2 sampling frequency
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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
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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
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To create arbitrary seismogram
• Becomes integral in the limit • Fourier Transform
– Computer: Fast Fourier Transform - FFT
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Exercise plots
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Sine_wave column 2
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Sine_wave column 2
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Sine_wave column 2 and 3
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Sine_wave column 2 and 3 sum
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Spectra, column 2
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Spectra, columns 2, 3
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Spectra, column 2, 3, 2 and 3 sum
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Multi_sine, individual columns
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Multi_sine, individual columns
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Multi_sine spectra
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Spike in time
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Spike in time, frequency
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Rock, sed, bog time series
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Rock spectra
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Rock (black), Sed (red), bog (blue)
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Spectral ratio sed/rock
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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
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Station LKWY, Utah
raw
Filtered2-19 Hz
Filtered twice
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Station LKWY, Utah
raw
Filtered2-19 Hz
Filtered twice
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Triggered earthquakes