1606:. Although this equation, as well the rest of the equations in section, does not explicitly include variables for a horizontal or vertical shift I think that is okay because a reader can probably figure out how to include such shifts themself. In additon, the inclusion of such variables in the formulas would add detail which I think would also clutter the formulas. I also ask that you not edit my posts, nor anyone elses except your own, on talk pages as doing so can misrpresent the posts original meaning. More details regarding editing other's talk page posts can be found at
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1195:- 2016. k = 1 to infinite can still work, however it requires a few changes. The approximation itself contains the Fourier series and the fourier coefficient (bn) as well as a method to automaticly sort out all the unnecessary bn coefficients (where bn = 0), of which there a lot. This is because the triangle wave best resembles a harmonic wave (compared to the sawtooth and square wave).
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Neither of the two formulas for x(t) actually give (a non-bandlimited version of) the waveform shown at the top of the page. They give some combination of incorrect amplitude, incorrect vertical shift, incorrect frequency, or incorrect phase. They are easy to fix but nonetheless it is misleading to
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Just realised the article was changed by an IP to the wrong version and your version is wrong also, I didn't read it properly, I assumed you were proposing a changing the wrong version I could see in the article. The change I have made in the article is to the correct version.
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684:. First of all, this device is obsolete so this is not actually a practical means of generating triangle waves. I am not at all sure that this belongs here in any case: it is aimed at the electronics hobbyist and as such is sailing close to
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I agree - I am trying to implement it in the time-domain and I was surprised to find the energy-output only half of what it should be. Had a "duh" moment when I saw the graph. I'll change it on the main page.
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I was just generating a triangle wave via additive synthesis and found this page unhelpful. What I ended up with was trivial: cos(wt)+cos(3wt)/9+cos(5wt)/25+... Any reason this isn't the expression shown?
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While doing some experiments, I actually noticed that a triangle wave has the odd members of the harmonics encountered in a square wave; that is, that in contains the harmonic frequencies 1, 5, 9, 13 aso.
692:, or else if they are not errors there is even more need for a reliable source. It also seems to have escaped the poster (as s/he did not link to it) that there is already an article on this device,
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The reason I like this better is because the constant k will be equal to the n'th-harmonic wave of the triangle wave, and seeing as this hasn't been changed I still think this has its relevance :)
1462:{\displaystyle y=2{\frac {a\arcsin \left(\sin \left({\frac {1}{\frac {\lambda }{4}}}\left({\frac {x\pi }{2}}-{\frac {\pi \left(h-{\frac {\lambda }{4}}\right)}{2}}\right)\right)\right)}{\pi }}+v}
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That's why the approximation was dependant on k = 0 to infinite it was using + instead of -, however it also means it can be rewritten to work with k = 1 to infinite. I personally use this:
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y=2 \frac{a \arcsin \left(\sin \left ( \frac{1}{ \frac{w}{4}} \left( \frac{x\pi} {2}-\frac{ \pi \left(h-\frac{w}{4} \right)}{2} \right) \right) \right)}{\pi}+v \right \rfloor</math: -->
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The root problem is the inbuilt number generator. Here's an example of two generators generating the same numbers: Odd numbers generator 1. Odd number = 2k-1, where k = 1,2,3,4,5...
1121:{\displaystyle x(t)={\frac {2}{a}}\left(2t-a\left\lfloor {\frac {2t}{a}}+{\frac {1}{2}}\right\rfloor \right)(-1)^{\left\lfloor {\frac {2t}{a}}+{\frac {1}{2}}\right\rfloor }}
959:{\displaystyle x(t)={\frac {2}{a}}\left(t-a\left\lfloor {\frac {t}{a}}+{\frac {1}{2}}\right\rfloor \right)(-1)^{\left\lfloor {\frac {t}{a}}+{\frac {1}{2}}\right\rfloor }}
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Just because it's shaped like a triangle wave doesn't mean it's a triangle wave. A true triangle wave has equal DC offset, and y=acos(sin(t)) is all above the y axis.
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It does appear that the summation in the
Harmonics section should start at 0, otherwise there is no fundamental and the series does not converge to a triangle wave.
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555:{\displaystyle {\begin{aligned}&{}={\frac {8}{\pi ^{2}}}\left(\sin(2\pi ft)+{1 \over 9}\sin(6\pi ft)+{1 \over 25}\sin(10\pi ft)+\cdots \right)\end{aligned}}}
383:{\displaystyle {\begin{aligned}&{}={\frac {8}{\pi ^{2}}}\left(\sin(2\pi ft)-{1 \over 9}\sin(6\pi ft)+{1 \over 25}\sin(10\pi ft)+\cdots \right)\end{aligned}}}
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I see that the equation that you provided does indeed work. Despite that, I am going to go ahead and remove your addition since a similar formula, specifically
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Shouldn't the approximation include normalization coefficient if I want to have it normalized ? Other pages like square, sawtooth all have this.
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Good catch, I have fixed it (and a few other things). Next time feel free to make the correction yourself, you don't need anyone's permission.
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https://www.wolframalpha.com/input/?i=sum+%28-1%29^k+*+sin%282+*+pi+*+t+*+%282+*+k+%2B+1%29%29+%2F+%282+*+k+%2B+1%29^2%2C+k%3D1+to+10
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https://www.wolframalpha.com/input/?i=sum+%28-1%29^k+*+sin%282+*+pi+*+t+*+%282+*+k+%2B+1%29%29+%2F+%282+*+k+%2B+1%29^2,+k%3D0+to+10
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The use of the abs(sawtooth) results in a range of 0-1, not -1 to 1 as implied in the first sentence of this section.
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I can play the longer audio sample, but when I press the 5 second sample play button, nothing happens. Safari/iOS.
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https://www.wolframalpha.com/input/?i=sum+(-1)%5E(k%2B1)*+(sin%E2%81%A1(2%CF%80(2k-1)t))%2F(2k-1)%5E2),+k%3D1+to+10
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on
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You should use k = 0 to 10, not k = 1 to 10, btw nice estimation of inf by 10 ;-)
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Yes. You can try it in Desmos to see if it works. I replace w with lambda.
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And it doesn't get any better with more iterations. Can somebody explain?
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137:Low-priority
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40:WikiProjects
1235:Hello all,
1161:Eyamseryath
686:WP:NOTHOWTO
641:—Preceding
205:91.155.86.4
112:Mathematics
103:mathematics
59:Mathematics
30:Start-class
1629:Categories
166:try it...
969:Be this?
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