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edited Jul 10, 2023 at 12:49

I had to make a bunch of band limited digital triangle waves recently, so I went to (where else) wikipedia for the equations.

I noticed that there is a constant amplitude scalar of 8/pi^2 (~.8106). And indeed this does bring the amplitude range down to about +/-1. The wikipedia article (https://en.wikipedia.org/wiki/Triangle_wave#HarmonicsThe wikipedia article) doesn't explain the theoretical reasoning for this but I would like to know why this is so.

I had to make a bunch of band limited digital triangle waves recently, so I went to (where else) wikipedia for the equations.

I noticed that there is a constant amplitude scalar of 8/pi^2 (~.8106). And indeed this does bring the amplitude range down to about +/-1. The wikipedia article (https://en.wikipedia.org/wiki/Triangle_wave#Harmonics) doesn't explain the theoretical reasoning for this but I would like to know why this is so.

I had to make a bunch of band limited digital triangle waves recently, so I went to (where else) wikipedia for the equations.

I noticed that there is a constant amplitude scalar of 8/pi^2 (~.8106). And indeed this does bring the amplitude range down to about +/-1. The wikipedia article doesn't explain the theoretical reasoning for this but I would like to know why this is so.

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asked Jul 14, 2020 at 2:14

dmedine

why does the additive synthesis method for a triangle wave require amplitude scaling by 8/pi^2?

I had to make a bunch of band limited digital triangle waves recently, so I went to (where else) wikipedia for the equations.

I noticed that there is a constant amplitude scalar of 8/pi^2 (~.8106). And indeed this does bring the amplitude range down to about +/-1. The wikipedia article (https://en.wikipedia.org/wiki/Triangle_wave#Harmonics) doesn't explain the theoretical reasoning for this but I would like to know why this is so.