Re: How do YOU handle this disparity in fft?

[Sergei Steshenko]

>________________________________
> From: Doug Stewart <address@hidden>
>To: Mike Miller <address@hidden> 
>Cc: address@hidden 
>Sent: Tuesday, February 11, 2014 2:35 PM
>Subject: Re: How do YOU handle this disparity in fft?
> 
>
[snip]
>I would like to explain that last paragraph a little more.
>
> Suppose you have a pure sine wave that is Fs/2. This means that it is sampled 
>2 times per cycle.
>
>Now if the first sample just happens to be at a zero crossing then all samples 
>will be at zero crossings, and the FFT will show 0 energy at that frequency. 
>
>Likewise If the first sample is at 1/4 Vmax then all samples will be at +- 1/4 
>Vmax, and the FFT will show 1/4 of the power that it should.
>
>
>I would likewise point out that the inverse FFT of these signals would be 0 
>for the first one, and a sawtooth  for the last one, not a sine wave.
>
>
>Finally: If you really  need to capture information about a certain frequency 
>then you must sample at a much higher rate than 2 time that frequency,
>
>I use a minimum of 8 or 10 samples per sine wave.
>
>IHTH
>
>
>Doug Stewart  
>
>

On saw tooth - even at lower, but not very low frequencies one rarely sees a 
sine wave.

DFT gives info on frequencies that represent FFT bins. By definition. I.e. DFT 
presents the signal as a finite sum of sine waves, and the sine waves have 
equally spaced frequencies.

DFT is also a block transform. I.e. an input signal window (set of N 
consecutive samples) is grabbed and the restored by inverse FFT signal is 
_periodic_ function with the N samples period while input signal is not at all 
necessarily periodic function.

That's why overlapping windows are used and the windows are typically Hamming 
or Hanning ones.The rule of thumb is: if you don't know what window to use, use 
the Hanning one.


Regards,
  Sergei.