🚀 go-pugleaf

Thanks Barry and Bob.

Barry, the idea is now concrete in my mind. I realized what I was missing
before. Thank you for the wonderful explanation.

David.

"Barry D. Jacobson" <bdjacobs@bellatlantic.net> wrote in message
news:Y6yL6.46346$Rg2.1574300@typhoon2.ba-dsg.net...
> Hi David:
>
> I think Bob's answer was not exactly what you were looking for, and was
> based on more complex mathematics. I think the answer to what is
> bothering you is the sampling rate issue. Matlab's FFT produces a set of
> frequency points which need additional information from you to interpret
> what frequency they correspond to in real life. The length of the
> sequence and the sampling rate determine the mapping to real life. For
> instance if you have a sequence of length L and sampling rate Fs then
> the highest real-life frequency (which is actually at about the midpoint
> of your Matlab FFT sequence) corresponds to 1/2 the sampling rate
> (Nyquist frequency). Each frequency point is then 2/L of the Nyquist
> freq. (The factor of 2 comes in because the second half of FFT sequence
> is mirror image of first and contains no new information for real
> signals. (These are called the negative frequencies which, in the usual
> DSP convention follow the positive freqs instead of preceeding them as
> in analog world. You can switch arrangement using FFTSHIFT command) The
> first frequency point is the DC value. The next is (Fs/2)/(L/2) or Fs/L
> the next is 2Fs/L, the next 3Fs/L until you reach midpoint (L/2) (Fs/L)
> or simply Fs/2, the highest possible freq. (next point begins the
> negative freqs). So if you have sequence 1000 points long and Fs is
> 100Hz, then first point is DC, second is .1 Hz, third is .2 Hz, fourth
> is .3 Hz, etc. (Note people normally use a power of 2 for length of FFT
> but this is only because FFT computation is faster that way. There is
> nothing else magic or more accurate about powers of 2, contrary to
> popular misconception.)
>
> When you use IFFT to transform back to time, you still have same issue
> of what point in real life time corresponds to each point in sequence.
> The answer here also depends on sampling rate. The first point is
> starting point T0 the second point is T0 plus 1/Fs, the next  T0 plus
> 2/Fs, etc. Since sampling rate figures into both calculations, the FFT
> and IFFT sequences are really not affected by whatever sampling rate you
> choose. The only difference is the mapping to real life. So matlab just
> takes one sequence as input and produces other sequence as output. It is
> up to you to interpret what they mean in your system. This is why many
> digital signal processing functions in matlab use a normalized sampling
> rate from 0 to 1 instead of your actual rate. You just multiply or
> divide by real sampling rate to convert between the two.
>
> I hope this clears things up.
>
> Barry Jacobson
> Harvard-MIT Division of Health Sciences and Technology
> bdj@mit.edu
>
> Maybe this
>
> David Page <david@REMOVE_SPAM.imhost.com> wrote in message
> news:eMqL6.71357$2U.31863845@news2.rdc2.tx.home.com...
> > I am a novice in Matlab. Please excuse if this question sounds silly.
> >
> > I am experimenting with fft and ifft function of Matlab. When I take a
> > fourier transform of a function, it fives me the frequency and its
> amplitude
> > (weight of the frequency) and does not contain any information about
> the
> > location of these frequencies.
> >
> > If the above is true, how can it reconstruct the whole signal again
> when
> > ifft is applied ? How does it remember the locations of the
> frequencies ?
> >
> > Thanks in advance.
> >
> >
>
>