Posted on Thursday, 12th April 2012
Please read sections 18.2.1-18.2.2 and post a comment.
Posted in Class | Comments (16)
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Posted on Thursday, 12th April 2012
Please read sections 18.2.1-18.2.2 and post a comment.
Posted in Class | Comments (16)
You must be logged in to post a comment.
April 15th, 2012 at 8:50 pm
I think I understand the basic concept of a periodogram acting as a plot of R^2 against frequency, but it’s not clear to me when these plots would be especially useful. Can you go through a few examples when it’s important to make these plots and what the plots themselves contribute?
April 16th, 2012 at 9:00 am
The Fourier analysis is difficult to me. For the LFP example, whict part represents LFP power?
April 16th, 2012 at 1:23 pm
No questions from me; very familiar with Fourier transforms and analysis.
April 16th, 2012 at 2:18 pm
In the equation for the periodogram in 18.25 on p524: I(ωj) = |d(ωj)|^2. Is this a typo? Should double bars denoting vector space have been used? Or is absolute value still necessary for some reason even though the term will be squared? (or is this notation for something else entirely?)
April 16th, 2012 at 7:53 pm
Can you go over more on how you derived equations 18.18 and 18.19?
April 16th, 2012 at 8:39 pm
Fourier analysis seems somewhat akin to fitting splines, in that both processes seem to involve decomposing a complex function into several smaller simple ones. In fitting splines, it can be beneficial to choose their relative locations by eye. Does Fourier analysis share this intuitive benefit (or any other, beyond the similar purpose) with spline fitting?
April 16th, 2012 at 9:07 pm
The text refers to detrending the series, “removing [slow varying trends] from the data before performing spectral analysis” (p. 527). Do you actually remove data? Why not include a parameter to allow for the trend?
April 16th, 2012 at 10:15 pm
I don’t understand how periodograms would be useful figures in stats, or why you’d want to smooth them. Can you explain what they show in a more intuitive way?
April 16th, 2012 at 10:41 pm
The Fourier analysis descriptions I have seen make the assumption that the signal is periodic and repeating, but you don’t seem to make that assumption because you only look at the signal in the interval [0,1]. Does this have consequences or is it just a different way of looking at the same thing?
April 16th, 2012 at 10:46 pm
I don’t really understand point 4 in the Fourier Analysis analysis. Can you explain the problem outlined within the first sentence of the point?
April 17th, 2012 at 1:31 am
I imagine it would be appropriate to use repeated fourier analysis on a stream of continuous data to represent changes over time. Is there a general rule about the length and sampling rate of time periods to perform this analysis on?
April 17th, 2012 at 7:48 am
Is the series of trig functions where k=1,2,3,…, really orthogonal? My impression was that you use powers of two to construct the Fourier transform… but it has been a very long time since I’ve looked at the basic construction of the Fourier transform.
April 17th, 2012 at 7:48 am
Would you ever take a measure of periodicity by doing linear regression on repeating segments of a curve?
I found the section on Fourier analysis very useful, thanks.
April 17th, 2012 at 7:52 am
I’m having trouble understanding exactly how we break down the signal into its harmonic components – can you go over this?
April 17th, 2012 at 8:00 am
We seem to just multiply the sine term in Euler’s formula (18.21) by i. Does that mean we divide it out after we perform all the calculations? Does this impact any of the math?
April 17th, 2012 at 8:23 am
FFT is the typical way to apply the Fourier transform… are there any pitfalls associated with FFT that we should know about, and are there sometimes other methods which should be used?