Re: Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg25601] Re: [mg25591] Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica
- From: "Carl K. Woll" <carlw at u.washington.edu>
- Date: Wed, 11 Oct 2000 03:50:40 -0400 (EDT)
- References: <200010100143.VAA14034@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
One idea is to use Collect. For example In[1]:= expr = a00 + a10 f[t] + a01 g[t] + a11 f[t] g[t] + a20 f[t]^2 + a21 f[t]^2 g[t]; In[2]:= f[t] = f1 Exp[+j w t] + f1Star Exp[-j w t]; g[t] = g1 Exp[+j w t] + g1Star Exp[-j w t]; Below I use Collect, with h acting as a wrapper to each of the harmonic coefficients. In[5]:= Collect[expr,{E^(_ t)},h] Out[5]= 3 j t w 2 E h[a21 f1 g1] + 2 j t w 2 E h[a20 f1 + a11 f1 g1] + 2 h[a21 f1Star g1Star] --------------------- + 3 j t w E h[a00 + 2 a20 f1 f1Star + a11 f1Star g1 + a11 f1 g1Star] + j t w E h[a10 f1 + a01 g1 + 2 2 a21 f1 f1Star g1 + a21 f1 g1Star] + 2 h[a20 f1Star + a11 f1Star g1Star] ---------------------------------- + 2 j t w E 2 h[a10 f1Star + a21 f1Star g1 + a01 g1Star + j t w 2 a21 f1 f1Star g1Star] / E Carl ----- Original Message ----- From: "AES" <siegman at stanford.edu> To: mathgroup at smc.vnet.net Subject: [mg25601] [mg25591] Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica > 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 >
- References:
- Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica
- From: AES <siegman@stanford.edu>
- Harmonic Analysis (Harmonic Matching) (Symbolic) in Mathematica