Hi Oleg, Yes, I should have addressed Dario - sloppy email reply on my part!
I will make a pass on the doc, and think about your factor of 2. - Julius On Sat, Jun 22, 2019 at 9:34 AM Oleg Nesterov <o...@redhat.com> wrote: > > Hi Julius, > > sorry for late reply, I was busy and didn't read emails from this list. > > On 06/17, Julius Smith wrote: > > > > Hi Oleg, > > > > I just now added a hilbert filter to filters.lib, and (probably what > > you really want) ssbf > > Me? ;) > > Heh. I know almost nothing about digital filters, to the point I don't even > know the terminology. Plus I forgot all the math I studied a long ago. > > So it was not easy to me to understand what fi.ssbf does and how it works. > But what I absolutely fail to understand is the new fi.hilbert filter. It > simply makes no sense to me, could you please explain? > > ------------------------------------------------------------------------- > So iiuc we have the "complex" (c,s) osscillator running at ma.SR/4 frequency > and > > ssbf = _,0 > : si.cmul(c,-s) // *conj(c,s), shift the spectrum by -SR/4 > : LPF(SR/4) // remove the negative part > : si.cmul(c,s); // shift it back by SR/4 > > OK, but how this > > // The Hilbert transform creates the imaginary part of an > // "analytic signal" $x(n)+j y(n)$ from its real part $x(n)$. > // > hilbert = ssbf : !,_; > > can work? > > Unless LPF above is ideal. And even if it was ideal, I think the correct > definition would be > > hilbert = ssbf : !,*(2); > > no? > > But it is not ideal, so I simply can't understand how/why this "hilbert" can > be used. > > Suppose that LPF above has FR(f) frequency response. To simplify, suppose that > FR(f) = 0 if f > SR/4. Then afaics > > cos(2*pi*F * t) : hilbert; > > will output > > abs(FR(SR/4 - F))/2 * sin(2*pi*F*t - arg(FR(SR/4 - F))); > > even if LPF is "flat", how can we avoid the phase error == arg(FR(SR/4 - F)) ? > > Thanks, > > Oleg. > > -- Julius O. Smith III <j...@ccrma.stanford.edu> Professor of Music and, by courtesy, Electrical Engineering CCRMA, Stanford University http://ccrma.stanford.edu/~jos/ _______________________________________________ Faudiostream-users mailing list Faudiostream-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/faudiostream-users
