There are a number of techniques available for estimating the frequency of a off-center sinusoid from the FFT bins around the one with peak magnitude. Can we also estimate the phase of the off-center sinusoid using similar methods? Would a legal approach be to find the frequency using the well-known methods and then interpolate the complex FFT data to get a complex response at the estimated frequency? Surely this has been done before. Thanks, John
FFT interpolation
Started by ●October 1, 2008
Reply by ●October 2, 20082008-10-02
On Oct 1, 8:33�pm, John <sampson...@gmail.com> wrote:> There are a number of techniques available for estimating the > frequency of a off-center sinusoid from the FFT bins around the one > with peak magnitude. Can we also estimate the phase of the off-center > sinusoid using similar methods? Would a legal approach be to find the > frequency using the well-known methods and then interpolate the > complex FFT data to get a complex response at the estimated frequency? > Surely this has been done before. > > Thanks, > > JohnHere's a couple of frequency estimation links: http://www.edn.com/archives/1994/030394/05df1.htm http://www.dspguru.com/howto/tech/peakfft2.htm If you can estimate the frequency accurately enough, then, based on your N point data record, you could compute the DFT for that one specific frequency.
Reply by ●October 2, 20082008-10-02
On Wed, 1 Oct 2008 20:47:10 -0700 (PDT), kevinjmcgee@netscape.net wrote:>On Oct 1, 8:33�pm, John <sampson...@gmail.com> wrote: >> There are a number of techniques available for estimating the >> frequency of a off-center sinusoid from the FFT bins around the one >> with peak magnitude. Can we also estimate the phase of the off-center >> sinusoid using similar methods? Would a legal approach be to find the >> frequency using the well-known methods and then interpolate the >> complex FFT data to get a complex response at the estimated frequency? >> Surely this has been done before. >> >> Thanks, >> >> John > >Here's a couple of frequency estimation links: > >http://www.edn.com/archives/1994/030394/05df1.htm >http://www.dspguru.com/howto/tech/peakfft2.htm > >If you can estimate the frequency accurately enough, then, based on >your N point data record, you could compute the DFT for that one >specific frequency.Ehh, the links on Grant's dspguru page cited above are broken to both Peter's page and my page, so I'll provide them here just for reference: http://home.comcast.net/~kootsoop/freqalgs.htm http://www.ericjacobsen.org/fe.htm If you look at Appendix B of 'On Local Interpolation of DFT Outputs' from the url just above, or directly here: http://www.ericjacobsen.org/FTinterp.pdf you'll see an interpolation method that seems to be what you're asking for. If you know the location of the interpolated output sample that you want, it's fairly straightforward to compute just that sample using the local samples around the peak. The methodology shown interpolates the full complex sample at whatever point desired, so you'll get both magnitude and phase. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Reply by ●October 2, 20082008-10-02
On Oct 1, 5:33�pm, John <sampson...@gmail.com> wrote:> There are a number of techniques available for estimating the > frequency of a off-center sinusoid from the FFT bins around the one > with peak magnitude. Can we also estimate the phase of the off-center > sinusoid using similar methods? Would a legal approach be to find the > frequency using the well-known methods and then interpolate the > complex FFT data to get a complex response at the estimated frequency? > Surely this has been done before.Yes you can interpolate phase directly from the FFT results, although it's better to either use FFTShift or to reference phase to the center of the FFT aperture by flipping some of the imaginary component sign bits. A non-bin centered sinusoid will be discontinuous at the ends of the FFT aperture, so the "phase" referenced to the start/end of the aperture won't mean the typical thing. Whereas the "evenness/oddness" of a sinusoid with respect to the aperture center will remain roughly the same across FFT bins, in the absence of noise or interference. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
Reply by ●October 2, 20082008-10-02
On 2 ���, 04:33, John <sampson...@gmail.com> wrote:> There are a number of techniques available for estimating the > frequency of a off-center sinusoid from the FFT bins around the one > with peak magnitude. Can we also estimate the phase of the off-center > sinusoid using similar methods? Would a legal approach be to find the > frequency using the well-known methods and then interpolate the > complex FFT data to get a complex response at the estimated frequency? > Surely this has been done before. > > Thanks, > > JohnYes. You can do it but you need that FFT window will overlap each other.
