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How to make a power spectra

How to make a power spectra. And discover something we don't understand well!. You will use a function I wrote, powerest.m, because it is easier to use and better documented than those in Matlab. function [pspecest,freqest,EDF,VAR]=powerest(tseries,taxis,nlength);

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How to make a power spectra

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  1. How to make a power spectra And discover something we don't understand well!

  2. You will use a function I wrote, powerest.m, because it is easier to use and better documented than those in Matlab. function [pspecest,freqest,EDF,VAR]=powerest(tseries,taxis,nlength); %return power spectrum [pspecest,freqest,EDF,VAR]=powerest(tseries,taxis,nseg); % % demeans the data before it runs. % % nseg is the length of the segments to be used in averaging % they will overlap by half their length and have a welsh window. % only works on evenly spaced data. frequency is in real, not angular % units. % % It also returns the scalar EDF, the estimated degrees of freedom for each % non-nyquist estimation, assuming Gauusian inputs as in Welch in Childer's % Modern Spectral Estimation % % it also returns the variance for each data point in the vector VAR % BOTH OF THESE ASSUME GAUSSIAN DISTRIBUTED RANDOM DATA!!!!! see Welch % in Childer.

  3. What are the inputs? [pspecest,freqest,EDF,VAR]=powerest(tseries,taxis,nseg); • tseries: A vector of data • taxis: the times the data was taken • nseg: the length of the averaging window in datapoints. Must be even! • What are the outputs? • pspecest: the power spectrum • freqest: the frequencies of pspecest, in units of 1/(units of taxis) • EDF, degrees of freedom in estimate of pspecest (you can ignore this for now) • VAR, the std2 of the error in pspecest.

  4. One big warning • data and time input into powerest.m must be vectors with 1 row and many columns • So if >> size(t) ans = 220751 1 >> size(BP) ans = 220751 1 • Then you would call powerest with [psd,freq,edf,var]=powerest(BP',t',nseg);

  5. So how do you use it? • I have several decades of atmospheric pressure from Duluth, MN:

  6. What periods am I interested in? • Annual period and smaller • So average over 3 to 5 year window • Good rule of thumb: window should be three to five times length of longest period you care about, if you can. %plot barometric pressure spectra clear all clf() load disw_BP_clean %compute power spectra nseg=1*24*365*3; [psd,freq,edf,var]=powerest(BP',t',nseg); %plot data semilogy(freq,psd,'linewidth',1) hold on xlabel('frequency, 1/period so 1/days') ylabel('power') %plot error semilogy(freq,psd-sqrt(var),'r--' ,freq,psd+sqrt(var),'r--')

  7. This gives you (without the error bars):

  8. How do we see the low frequencies? • axis command returns axis limits and sets them • takes and returns: [xmin xmax ymin ymax] • So to get the existing limits, and set the x axis limits to be between 0 and 1/90 days-1 (explain) temp = axis; axis([0 1/90 temp(3:4)]); % explain! • Not much interesting at low frequency • Note annual. • Define red! • What would I do if I cared more about low frequencies?

  9. What is up at high frequencies? • explain what the spikes mean • What is an "Atmospheric tide"?

  10. What does the tide look like in time? • how did I calculate it? • remember GMT! • What causes it? • Not super strong! • Rule of thumb that will be important in homework. If you have a signal that repeats over a period P, it will show up in the spectra at • Periods P, P/2, P/3, P/4,P/5 and so forth • Frequency 1/P,2/P,3/P,4/P,5/P and so forth. • Explain!

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