Like this http://www.wolframalpha.com/input/?i=1-2*%28%28x-1%29+mod+1%29%2C+tanh%286*x%29%2Ftanh%286%29+from+-1+to+1 ? Doesn't seem to work http://www.wolframalpha.com/input/?i=1-2*%28%28x-1%29+mod+1%29%2C+tanh%286*x%29%2Ftanh%286%29+from+-1+to+1 Kalle Quoting "Victor Lazzarini" : > Shouldn't the tanh be offset in relation to the sawtooth ramp? This > would place the > transition region of the sigmoid at the sawtooth discontinuity. I > think it could work better. > In particular, there seems to be a DC component for a < pi > In other words, this : > > a1 phasor p4 > a1 = 2*a1 - 1 > ka = 10 > atanh tablei ka*a1, 2, 1, 0.5 > kscal tablei ka, 2, 1 > asig = (a1 - atanh/kscal)*0dbfs/4 > > > with > > f2 0 65537 "tanh" -3.14 +3.14 > > > On 29 Mar 2011, at 01:09, kalleaho@mappi.helsinki.fi wrote: > >> And integrating gives parabolic wave >> >> (2*x-1)^2/2-ln(cosh(a*(2*x-1)))/(a*tanh(a)) >> >> which can be used to get variable duty cycle triangle waves. >> When the formula for sawtooth is defined so that x goes from -1 to >> 1 it is rather simple >> >> x-tanh(a*x)/tanh(a) >> >> and parabolic wave is then >> >> 1/2*x^2-ln(cosh(a*x))/(a*tanh(a)) >> >> Other sigmoids could be used in the place of tanh I guess. >> >> Kalle >> >> >> Quoting Victor.Lazzarini@nuim.ie: >> >>> I don't think so. Interesting. >>> >>> Victor >>> >>> ----- Original Message ----- >>> From: kalleaho@mappi.helsinki.fi >>> Date: Monday, March 28, 2011 11:54 pm >>> Subject: [Csnd] A remarkable formula >>> To: csound@lists.bath.ac.uk >>> >>>> Hi, >>>> >>>> I got inspired by Victor's tanh() ideas and found this >>>> remarkable formula >>>> >>>> 2*x-1-tanh(a*(2*x-1))/tanh(a) >>>> >>>> If x is a phasor going from 0 to 1, this gives an approximate >>>> sawtooth >>>> with roughly 2*a harmonics, when a is about 3.5 or greater. Try it! >>>> >>>> Is this known? >>>> >>>> Kalle >>>> >>>> >>>> >>>> >>>> Send bugs reports to the Sourceforge bug tracker >>>> https://sourceforge.net/tracker/?group_id=81968&atid=564599 >>>> Discussions of bugs and features can be posted here >>>> To unsubscribe, send email sympa@lists.bath.ac.uk with body >>>> "unsubscribe csound" >>>> >>> >>> Dr Victor Lazzarini, Senior Lecturer, Dept. of Music, >>> National University of Ireland, Maynooth >>> >>> >>> >>> Send bugs reports to the Sourceforge bug tracker >>> https://sourceforge.net/tracker/?group_id=81968&atid=564599 >>> Discussions of bugs and features can be posted here >>> To unsubscribe, send email sympa@lists.bath.ac.uk with body >>> "unsubscribe csound" >>> >>> >> >> >> >> >> Send bugs reports to the Sourceforge bug tracker >> https://sourceforge.net/tracker/?group_id=81968&atid=564599 >> Discussions of bugs and features can be posted here >> To unsubscribe, send email sympa@lists.bath.ac.uk with body >> "unsubscribe csound" >> > > Dr Victor Lazzarini > Senior Lecturer > Dept. of Music > NUI Maynooth Ireland > tel.: +353 1 708 3545 > Victor dot Lazzarini AT nuim dot ie > > > > > > Send bugs reports to the Sourceforge bug tracker > https://sourceforge.net/tracker/?group_id=81968&atid=564599 > Discussions of bugs and features can be posted here > To unsubscribe, send email sympa@lists.bath.ac.uk with body > "unsubscribe csound" > > > Send bugs reports to the Sourceforge bug tracker https://sourceforge.net/tracker/?group_id=81968&atid=564599 Discussions of bugs and features can be posted here To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"