Hi Donovan.

FFT is not a _continuous_ spectrum of an infinitely long sampling of a signal.
In that case you would have an infinitely thin, infinitely high spike at 3Hz and
nothing else.

You may have an exactly 3Hz pin in the spectrum, but unless your 3Hz is an
entirely clean sine wave, it will not show as one pin. Even with a 3Hz that is clean,
your FFT is handling a finite number of points - therefore you are not getting an
integral number of full periods of your 3Hz, and your signal may be non-
symmetrical.

Since FFT handles your N samples of a signal as if it were a closed loop, repeating
infinitely, you will get a discontinuity at t=0. This also has to be modelled with a
frequency content.

If you,  with MatLab, construct a 3Hz signal that is symmetrical (easy way, make a
spike at 3 Hz and IFFT) you will notice it is symmetrical.

If you want to determine what frequencies you actually have in a spectrum, you
need to look at formant frequencies. Speech analysis and synthesis has the
answers.

You should rather see FFT as a way of determining how to CONSTRUCT the
LOOPED, SAMPLED SECTION signal you are analyzing as a linear combination of
sine wave functions.

Kent

> Hello,
>
> I'm hoping someone can give me an intuitive feeling for what an FFT does and
> how to interprete data in the frequency domain.  I am using Matlab to do an
> FFT on sampled data and am having trouble understanding the resulting
> frequency domain picture.
>
> Here is some 'things' that are bugging me:
>
> 1. if I sample a sine wave with a frequency of 3Hz at 10Hz then the
> resulting frequency domain picture shows
>     a 'spike' at 3Hz, but there is noticable frequency content around 3Hz.
> I understand the 'spike' at 3Hz, but
>     don't understand why there is so much 'noise' as I am sampling at twice
> the highest frequency.
>
> 2. say I have completely random data, except that every second on the second
> the data is a 1.  does this mean I have frequency content at 1Hz? and no
> frequency content elsewhere?
>
>
> Regards,
> Donovan (A confused EE student)
>
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