Square + triangle = sine (almost)
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From: Harold Larsen on 6 Mar 2010 22:12 If a squarewave contains all odd harmonics of the fundamental frequency, and a triangle all even, will I get ALL harmonics if I mix the two waveforms? It looks like a cross between a squarewave and sinewave. I have not seen any tech references to the practical value of this. Does it have any? For example, to roughly approximate a sinewave without filtering. Harold Larsen
From: Phil Allison on 6 Mar 2010 22:31 "Harold Larsen" > > If a squarewave contains all odd harmonics of the fundamental > frequency, and a triangle all even, ** Sorry - that is WRONG . A triangle wave contains only odd harmonics too. http://en.wikipedia.org/wiki/Triangle_wave A "sawtooth" wave contains all integer harmonics. ..... Phil
From: Ron Tanner on 6 Mar 2010 23:04 On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison" <phil_a(a)tpg.com.au> wrote: > >"Harold Larsen" >> >> If a squarewave contains all odd harmonics of the fundamental >> frequency, and a triangle all even, > > > ** Sorry - that is WRONG . > > A triangle wave contains only odd harmonics too. > >http://en.wikipedia.org/wiki/Triangle_wave > >A "sawtooth" wave contains all integer harmonics. > OK thanks for the pull-up, but how about using a triangle-square wave mix, in place of a filter, to simulate a sinewave . I have not seen that method applied or described anywhere, but it makes a fair approximation, at least to my eye. Harold Larsen
From: Phil Allison on 6 Mar 2010 23:10 "Ron Tanner" "Phil Allison" > >>"Harold Larsen" >>> >>> If a squarewave contains all odd harmonics of the fundamental >>> frequency, and a triangle all even, >> >> >> ** Sorry - that is WRONG . >> >> A triangle wave contains only odd harmonics too. >> >>http://en.wikipedia.org/wiki/Triangle_wave >> >>A "sawtooth" wave contains all integer harmonics. >> > > OK thanks for the pull-up, but how about using a triangle-square wave > mix, in place of a filter, to simulate a sinewave . > > I have not seen that method applied or described anywhere, but it > makes a fair approximation, at least to my eye. > ** Maybe you need better eyes. Ever noticed how sine waves are flat topped and pass through zero at a 45 degree angle ? Not much like your hut with pitched roof wave....... ...... Phil
From: D from BC on 6 Mar 2010 23:21
In article <4b9324ee.4432562(a)news.tpg.com.au>, rontanner(a)esterbrook.com says... > > On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison" <phil_a(a)tpg.com.au> > wrote: > > > > >"Harold Larsen" > >> > >> If a squarewave contains all odd harmonics of the fundamental > >> frequency, and a triangle all even, > > > > > > ** Sorry - that is WRONG . > > > > A triangle wave contains only odd harmonics too. > > > >http://en.wikipedia.org/wiki/Triangle_wave > > > >A "sawtooth" wave contains all integer harmonics. > > > > OK thanks for the pull-up, but how about using a triangle-square wave > mix, in place of a filter, to simulate a sinewave . > > I have not seen that method applied or described anywhere, but it > makes a fair approximation, at least to my eye. > > Harold Larsen This reminds of the XR2206 chip that makes square, triangle and sine using analog technology. |