Re: Distortion Measurement, use FFT or not ?

Rune Allnor wrote:
On 2 Feb, 12:01, Adam S <not.valid@nosuchaddress> wrote:
Hi Bharat

I'm a bit confused as to how interpolation of FFT bin magnitudes can be
used to pin point the magnitude of tone laying at a frequency between
those bins.
As I understand, when a signal is not exactly a multiple of the sampling
frequency then the power of that signal is distributed across
surrounding FFT bins.

Correct.

So if one takes the average power (sum of squares
of magnitudes) over these bins then they will get almost the same power
as from a single bin when the input frequency is an exact multiple of
Fs.

Correct.

I just wrote a small test program to check this for myself.

Good.

Experimentally I found that when using a Hanning window the useful side
bins only extended about +-2 bin either side of the centre bin. The
spectrum power across these 5 bins showed to add up to about 0.9997 of
the total power.

I've heard FFT interpolation being used to estimating the frequency of a
single tone, but not its magnitude.

The purpose of the windowing functions is to suppress
sidelobes, but there are no guarantees that they preserve
magnitude or power.

You started this thread with a question about measuring
nonlinear responses in a test system. There is a chance that
you will have to settle for a method which maps relative
distribution of power between spectrum components, leaving
absolute powers levels out.

If you check out the book I mentioned in a different post
you might find something that answers the question you
started out from.


Ok, I'll check out "Random Data" by Bendat & Piersol next time I'm near my local university library. You are correct in that I don't have much hope in finding absolute amplitudes of spectral components. Fortunately for distortion measurement, only relative amplitudes are required.

I had to asked a question about amplitude estimation because there was no obvious way of determining amplitude of a tone at arbitrary frequency from its DFT output. Taking the total power of a few DFT bins either side of the peak, is the only method conceiveable to me for estimating single tone amplitudes. Applying windowing to the input data reduces side lobes witch in tern reduces number of bins needed when summing the total power across those bins.

As Jerry pointed out, why not remove the fundamental and apply a FFT on what is remaining. Seems like an obvious solution to reducing affect of side lobes from the fundamental and making harmonics stand out more easily.
.

Relevant Pages

  • Re: Distortion Measurement, use FFT or not ?
    ... surrounding FFT bins. ... So if one takes the average power (sum of squares ... single tone, but not its magnitude. ...
    (comp.dsp)
  • Re: Distortion Measurement, use FFT or not ?
    ... I'm a bit confused as to how interpolation of FFT bin magnitudes can be ... surrounding FFT bins. ... of magnitudes) over these bins then they will get almost the same power ...
    (comp.dsp)
  • Re: Calculation FFT...
    ... blocks of rectangularly windowed FFTs. ... If you are looking for something with "wider" bins you need to do ... If you are only interested in power, you can form sums of the powers ... Dale B. Dalrymple ...
    (comp.dsp)
  • Re: Distortion Measurement, use FFT or not ?
    ... I'm a bit confused as to how interpolation of FFT bin magnitudes can be used to pin point the magnitude of tone laying at a frequency between those bins. ... when a signal is not exactly a multiple of the sampling frequency then the power of that signal is distributed across surrounding FFT bins. ...
    (comp.dsp)
  • Re: Distortion Measurement, use FFT or not ?
    ... I'm a bit confused as to how interpolation of FFT bin magnitudes can be used to pin point the magnitude of tone laying at a frequency between those bins. ... when a signal is not exactly a multiple of the sampling frequency then the power of that signal is distributed across surrounding FFT bins. ...
    (comp.dsp)