It's not the discontinuity -- it's the bin values.
If the desired frequency is not an EXACT multiple of the bin value you'll
get a reduced peak and leakage....one of the downfalls of DFTs. As Joe
noted a larger FFT would have more resolution but is likely not going to
improve things.
A rectangular window preserves minimum main lobe width at the expense of
higher leakage. Other windows will increase peak value and have reduced
leakage but also have less accuracy due to spreading of the main peak. The
leakage should not be much of a factor for this frequency calibration
unless you are borderline on the peak SNR where a Triangular window would
be best but picks up less then 1dB over a rectangular window -- see
http://www.bores.com/courses/advanced/windows/files/windows.pdf
There's already a fit function in the code which is giving better than the
bin width in accuracy. Could be improved on slightly perhaps with a cubic
spline but looks good enough as-is to me and I doubt a spline would really
improve much at all.
On my freq cal I see numerous RMS entries < 0.1Hz -- Average RMS is 0.27 --
so the peak fit being done is doing pretty well.
de Mike W9MDB
On Mon, Jan 9, 2017 at 5:23 PM, Steven Franke <s.j.fra...@icloud.com> wrote:
> Since Joe is probably eating dinner at the moment…
>
> With 55296 point FFT, a 1600 Hz tone (7.5 sa/period) has 55296/7.5=7372.8
> cycles in a record - so there is an endpoint discontinuity (i.e. a
> discontinuity between the first and last points of the record).
>
> A 1500 Hz tone (8 samples per period) has 6912 cycles in a record, so
> there’s no endpoint discontinuity.
>
> I think that what you’re seeing is the result of using a non-windowed FFT.
> It’s easily addressed, if necessary.
>
> Steve
>
>
> > On Jan 9, 2017, at 11:07 PM, Bill Somerville <g4...@classdesign.com>
> wrote:
> >
> > On 09/01/2017 22:28, Bill Somerville wrote:
> >> ... for sure the three
> >> magnitudes going into peakup are much flatter when the error is greater
> ...
> > Hi Joe,
> >
> > Here are some examples, these are DFT magnitudes (s vector) for five
> > bins around a 1500Hz tone:
> >
> > 0.107814305 0.175234795 9.38052759E-02 17124122.0
> 8.95743668E-02 8.78201425E-02 4.62990999E-02
> > 7.97733366E-02 0.128112748 0.307582766 17126434.0
> 0.167245105 1.00381924E-02 1.45341307E-02
> > 5.32349795E-02 7.02278912E-02 0.130553111 17125166.0
> 0.135780737 6.56466857E-02 0.104219861
> >
> > and here is the same for a 1600Hz tone:
> >
> > 79235.5156 191998.594 973516.500 15560843.0
> 432274.188 128688.836 60769.3555
> > 79641.3359 192280.516 972233.375 15562208.0
> 432276.500 128727.242 60738.6406
> > 79411.3125 192080.391 972825.562 15561087.0
> 431534.812 128623.734 60596.7227
> >
> > These numbers are from print *, s(ipk-2:ipk+2) with DF set to the tone
> > and FTol at 1000Hz.
> >
> > 73
> > Bill
> > G4WJS.
> >
> >
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