Comments on: Tues Apr 17 http://www.stat.cmu.edu/~kass/smnp/?p=123 Thu, 26 Apr 2012 14:07:02 +0000 hourly 1 http://wordpress.org/?v=3.0.4 By: Rex Tien http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-326 Rex Tien Tue, 17 Apr 2012 13:23:47 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-326 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? 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?

]]> By: Scott Kennedy http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-325 Scott Kennedy Tue, 17 Apr 2012 13:00:47 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-325 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? 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?

]]> By: Thomas Kraynak http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-324 Thomas Kraynak Tue, 17 Apr 2012 12:52:20 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-324 I'm having trouble understanding exactly how we break down the signal into its harmonic components - can you go over this? I’m having trouble understanding exactly how we break down the signal into its harmonic components – can you go over this?

]]> By: David Zhou http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-323 David Zhou Tue, 17 Apr 2012 12:48:53 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-323 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. 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.

]]> By: Matt Bauman http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-322 Matt Bauman Tue, 17 Apr 2012 12:48:07 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-322 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. 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.

]]> By: Matt Panico http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-321 Matt Panico Tue, 17 Apr 2012 06:31:44 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-321 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? 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?

]]> By: Noah http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-320 Noah Tue, 17 Apr 2012 03:46:54 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-320 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? 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?

]]> By: Ben Dichter http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-319 Ben Dichter Tue, 17 Apr 2012 03:41:43 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-319 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? 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?

]]> By: Sharlene Flesher http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-318 Sharlene Flesher Tue, 17 Apr 2012 03:15:40 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-318 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? 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?

]]> By: Amanda Markey http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-317 Amanda Markey Tue, 17 Apr 2012 02:07:38 +0000 http://www.stat.cmu.edu/~kass/smnp/?p=123#comment-317 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? 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?

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