Re: FFT of non-integer waveform

Sounds to me like you're talking about (from the frequency domain point
of view) a sine wave with a frequency that does not lie on the center
frequency of a given FFT bin, correct? I'm assuming your problem is
that you are getting smearing in the frequency domain when looking at
this kind of signal after taking the FFT. Is this correct?

The simplest solution is to window the data in the time domain before
taking the FFT. There are many kinds of windows. Hamming, Hanning, and
Blackman are common ones. This won't pinpoint the frequency of the sine
wave, but it will reduce the spectral smearing significantly and
isolate the energy to a set of bins of interest.

Bob

Ross Clement (Email address invalid - do not use) wrote:
Hi everyone. Suppose I have a sound sample digitised at say 44.1khz.
Say that I have identified a single cycle of a waveform and wish to
perform a fft so that I can understand the spectral content of the
waveform. What happens if I believe that the waveform starts in between
two of the samples and ends between another two samples. How do I then
use a discrete fourier transform to measure the spectral content. One
potential method is to ignore the non-integer starts, and fourier
transform the waveform using the nearest samples from the beginning and
the end. Another simple method would be to resample the waveform to a
much higher sampling rate so that I at least get nearer to the true
start and finish of the waveform.

Are there any techniques for this kind of problem?

Cheers,

Ross-c

.

Relevant Pages

  • Re: FFT of non-integer waveform
    ... Say that I have identified a single cycle of a waveform and wish to ... You have "identified a single cycle of the waveform".... ... FFT the padded sequence. ... the spectrum will be interpolated by a factor of 10. ...
    (comp.dsp)
  • Re: anti-aliasing
    ... The adc will take a bunch of samples, ... If the sine wave is of a sufficently low frequency WRT to full sample time, then any given sub-section of that sine would be samples, giving obvious errors. ... If it is a complex waveform signal, that might not be a useable solution. ... "small" dithering of the sampling periodicity will not help; it might be useful when the input periodocity is near one of the harmonics of the sampling rate. ...
    (sci.electronics.design)
  • Re: I found the holy grail that explains audiophile beliefs
    ... steady amplitude sine wave it does not work with a decaying sine wave, like Cymbols clanging, unless the decay rate is slow enough to build up a number of samples. ... waveform can be thought of as a small section of a longer repeating waveform. ... While it may be reconstructed within reason, a side by side comparison of the original analog and the digitized output will show differences, distortion, phase delay, and some sideband spikes a KHz or so on either side of the desired waveform. ... The spikes were post digital filter so it could have been due to the switched capacitor clock getting through and causing strange things. ...
    (rec.audio.pro)
  • Re: Digital sine wave generation
    ... equal phase spacing, I'm very interested. ... generates a waveform that is a stepped sine approximation. ... Maybe I should've written "that do sine wave synthesis and do a good ...
    (sci.electronics.design)
  • Re: Tone generator
    ... 18kHz tone, in fact a rather bizarre jagged sawtooth. ... What you are looking at is the filtered output, not the original waveform. ... You're right that the sine wave is smooth because of low pass filtering, but you're wrong that it's not a pure sine wave. ... So long as the reconstruction filter is of a reasonable quality then the 18 kHz sine wave will be as pure as any other sine wave anywhere from DC to 20 kHz. ...
    (uk.comp.sys.mac)