Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg25591] Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica*From*: AES <siegman at stanford.edu>*Date*: Mon, 9 Oct 2000 21:43:31 -0400 (EDT)*Organization*: Stanford University*Sender*: owner-wri-mathgroup at wolfram.com

How can one do symbolic harmonic analysis (aka "harmonic matching") in Mathematica? That is, I'd like to insert sinusoidal functions f[t] and g[t] written as f[t] = f1 Exp[+j w t] + f1Star Exp[-j w t] g[t] = g1 Exp[+j w t] + g1Star Exp[-j w t] into a polynomial in f[t] and g[t], e.g. expr = a00 + a10 f[t] + a01 g[t] + a11 f[t] g[t] + a20 [f[t]^2 + a21 f[t]^2 g[t] + and so on and then pull out the individual harmonic components, i.e. the Exp[+j w t], Exp[-j w t], Exp[+2 j w t], Exp[-j w t], etc., components. (This may not be what some people call harmonic analysis, but it's a common approach in engineering analysis of nonlinear systems.) A simple way to do this? (Note: the coefficients may themselves be expressions that contain factors like Exp[constant] -- though not t explicitly.] Thanks, AES

**Follow-Ups**:**Re: Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica***From:*"Carl K. Woll" <carlw@u.washington.edu>