Numeric Sequence & Inverse Discrete Fourier Transform

[Vijai Kalyan]

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.

[SteveSmith]

Hi Vijai,
If you take the Fourier Transform of any real signal, you will always se
this kind of symmetry in the frequency spectrum. This is simply how the F
works, and tells you nothing about the particular signal you are dealin
with. Here's a link if you would like a more detailed explanation. Kee
trying!
Regards,
Steve


http://www.dspguide.com/ch12/1.htm

[Rick Lyons]

On Sat, 4 Oct 2008 13:22:34 -0700 (PDT), Vijai Kalyan
<[email protected]> 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
>c

I 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-]