On Sep 24, 4:53�pm, zebra <e...@eastwestsounds.com> wrote:> > you should try to design the non-linear operation or waveshaper so > > that it inherently does not create any frequency components above fs/ > > 2. �at the �fs at which it is operating... > > oh right, for sure > > there is the always handy fact that an n-th order polynomial produces > up to nth order harmonics. so upsample by a factor of n... >bingo!

# Upsampling problem

Started by ●September 21, 2008

Reply by ●September 25, 20082008-09-25

Reply by ●September 25, 20082008-09-25

zebra <ezra@eastwestsounds.com> writes:> there is the always handy fact that an n-th order polynomial produces > up to nth order harmonics. so upsample by a factor of n...I don't recall seeing that anywhere. Do you have a reference? Or is it so simple it's obvious? :) -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com

Reply by ●September 25, 20082008-09-25

Randy Yates wrote:> zebra <ezra@eastwestsounds.com> writes: > >> there is the always handy fact that an n-th order polynomial produces >> up to nth order harmonics. so upsample by a factor of n... > > I don't recall seeing that anywhere. Do you have a reference? Or is it > so simple it's obvious? :)It simply falls out in the algebra. Take a signal: s(t) = sin (2 pi f t) and substitute it for x in a polynomial like: p(x) = a + b x + c x^2 + ... n x^n Once you expand out the trig identities you will find the maximum output component by inspection. Erik -- ----------------------------------------------------------------- Erik de Castro Lopo ----------------------------------------------------------------- "It seems you are presuming a Waterfall model of development here. We're not doing the Waterfall, we're doing the Whirlpool." -- Larry Wall on Perl6 "Perl is circling the drain, that's for sure..." -- llimllibon reddit

Reply by ●September 25, 20082008-09-25

Erik de Castro Lopo <nospam@mega-nerd.com> wrote:>Randy Yates wrote:>> zebra <ezra@eastwestsounds.com> writes:>>> there is the always handy fact that an n-th order polynomial produces >>> up to nth order harmonics. so upsample by a factor of n... >> >> I don't recall seeing that anywhere. Do you have a reference? Or is it >> so simple it's obvious? :)>It simply falls out in the algebra. Take a signal: > > s(t) = sin (2 pi f t) > >and substitute it for x in a polynomial like: > > p(x) = a + b x + c x^2 + ... n x^n > >Once you expand out the trig identities you will find the >maximum output component by inspection.I see a distinction between the "maximum output component" of a polynomial function being n-th order, and the polynomial function having "up to n-th order harmonics". Steve

Reply by ●September 25, 20082008-09-25

Erik de Castro Lopo <nospam@mega-nerd.com> writes:> Randy Yates wrote: > >> zebra <ezra@eastwestsounds.com> writes: >> >>> there is the always handy fact that an n-th order polynomial produces >>> up to nth order harmonics. so upsample by a factor of n... >> >> I don't recall seeing that anywhere. Do you have a reference? Or is it >> so simple it's obvious? :) > > > It simply falls out in the algebra. Take a signal: > > s(t) = sin (2 pi f t) > > and substitute it for x in a polynomial like: > > p(x) = a + b x + c x^2 + ... n x^n > > Once you expand out the trig identities you will find the > maximum output component by inspection.Oh yeah. Cool - thanks Erik. -- % Randy Yates % "She tells me that she likes me very much, %% Fuquay-Varina, NC % but when I try to touch, she makes it %%% 919-577-9882 % all too clear." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com

Reply by ●September 25, 20082008-09-25

Steve Pope wrote:> I see a distinction between the "maximum output component" of > a polynomial function being n-th order, and the polynomial function > having "up to n-th order harmonics".Not "up to n-th order harmonics", "up to and including n-th order harmonics". Erik -- ----------------------------------------------------------------- Erik de Castro Lopo ----------------------------------------------------------------- "And MS thinks Linux is vulnerable to forking? 95, 95 OEM SR2, 98, 98SE, ME, NT, 2000, Bob, .NET, CE, Datacenter, Server, Adv. Server, and now Web Server, sheesh." -- BTS on LinuxToday.com