[haskell-art] Is The Amplitude Scaling Formula in Dodge/Jerse Correct? (fwd)

[Henning Thielemann]

---------- Forwarded message ----------
Date: Mon, 20 Aug 2012 11:07:09 +0200 (CEST)
From: Henning Thielemann <***@henning-thielemann.de>
To: Haskell Media <***@gmail.com>
Subject: Re: [haskell-art] Is The Amplitude Scaling Formula in Dodge/Jerse
Correct?

f0 is the fundamental. Dodge defines f0 to be the fundamental when he was
talking about distortion
techniques a few pages before this...

That's very strange because the coefficient 1/2 for the direct current partial
is very common since it matches our intuition of amplitude of sine waves and
direct current. The complex Fourier series is simpler in this respect because
the coefficients are all equally weighted.

https://en.wikipedia.org/wiki/Fourier_series#Fourier.27s_formula_for_2.CF.80-periodic_functions_using_sines_and_cosines

My guess is that the scaling factor they used in the book was specifically
for Chebyshev polynomials.
Still not clear on why it scales up to 2.... Would be nice to have a general
scaling formula for additive
synthesis (if the "Dodge" amplitude scaling isn't the general formula
already).

Btw. for computing the power of the signal you do not need the harmonics at
all. You can simply compute the L2 norm of the signal thanks to Parseval's
identity.

https://en.wikipedia.org/wiki/Parseval's_identity