Hello Everyone, I am trying to analyze a sequence of integral values that come from an unknown but potentially non-random source. At the least, the series seem to fail the chi-square test. I had an idea for analyzing the sequence by applying a fourier transform on the values. The fourier transform seems to indicate that the sequence could be periodic. For example, in the fourier transform, the values are c' c1 c2 c3 c4 c5 0 -c5 -c4 -c3 -c2 -c1 c I felt that this could indicate that the series is not really random. So, I extrapolated the values as c' c1 c2 c3 c4 c5 0 -c5 -c4 -c3 -c2 -c1 c c1 c2 c3 c4 c5 0 -c5 -c4 -c3 -c2 -c1 c and tried to apply the inverse fourier transform. I end up with a series of values that bear no relation to the input. Overlay plots of the input sequence and the values from the inverse FT do not seem to indicate any relation either. I am not a signal processing guy, so not sure what I am doing incorrect here. Is my method of analysis correct? Is it possible to find for example, the possible outline of the function that is generating the sequence? Thanks, Vijai.

# Numeric Sequence & Inverse Discrete Fourier Transform

Started by ●October 4, 2008

Reply by ●October 4, 20082008-10-04

Hi Vijai, If you take the Fourier Transform of any real signal, you will always see this kind of symmetry in the frequency spectrum. This is simply how the FT works, and tells you nothing about the particular signal you are dealing with. Here's a link if you would like a more detailed explanation. Keep trying! Regards, Steve http://www.dspguide.com/ch12/1.htm

Reply by ●October 5, 20082008-10-05

On Sat, 4 Oct 2008 13:22:34 -0700 (PDT), Vijai Kalyan <vijai.kalyan@gmail.com> wrote:>Hello Everyone,Hello Hi Vijai, I'll bet someone here can help you if you're willing to give us more information.>I am trying to analyze a sequence of integral values that come from an >unknown but potentially non-random source. At the least, the series >seem to fail the chi-square test.What does the word "analyze" mean? Also, does the word "integral" mean "integer"? Are the samples in your sequence real numbers (as opposed to complex numbers)?> >I had an idea for analyzing the sequence by applying a fourier >transform on the values. The fourier transform seems to indicate that >the sequence could be periodic. For example, in the fourier transform, >the values are > >c' >c1 >c2 >c3 >c4 >c5 >0 >-c5 >-c4 >-c3 >-c2 >-c1 >cI can only guess at what your notation means, but that above sequence can only make sense if the input samples to your Fourier transform (computed as a discrete Fourier transform) are complex-valued. I'm assuming that "-c3" means "minus c3", and that "c'" and "c" are two different numbers.>I felt that this could indicate that the series is not really random. >So, I extrapolated the values as > >c' >c1 >c2 >c3 >c4 >c5 >0 >-c5 >-c4 >-c3 >-c2 >-c1 >c >c1 >c2 >c3 >c4 >c5 >0 >-c5 >-c4 >-c3 >-c2 >-c1 >c > >and tried to apply the inverse fourier transform. I end up with a >series of values that bear no relation to the input. Overlay plots of >the input sequence and the values from the inverse FT do not seem to >indicate any relation either.I can believe that the above "extrapolation" produced gibberish time-domain data. That extrapolation does not make sense to me.>I am not a signal processing guy, so not sure what I am doing >incorrect here. Is my method of analysis correct? Is it possible to >find for example, the possible outline of the function that is >generating the sequence?What do the words "possible outline of the function" mean? Can you tell us exactly what it is about your sequence that you're trying to determine? [-Rick-]