Separating AC Components From DC
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From: Bret Cahill on 5 Jun 2010 23:38 Several functions in an equation have ac and dc components. If all the dc is filtered out of the functions for ac only and then all the ac out of the dc, will the equation hold for just the dc and just the ac? The equation doesn't do anything more than add, multiply and divide the functions. Bret Cahill
From: Tim Little on 6 Jun 2010 02:50 On 2010-06-06, Bret Cahill <BretCahill(a)peoplepc.com> wrote: > Several functions in an equation have ac and dc components. If all > the dc is filtered out of the functions for ac only and then all the > ac out of the dc, will the equation hold for just the dc and just > the ac? > > The equation doesn't do anything more than add, multiply and divide > the functions. No. Almost any nontrivial set of functions and equations would provide a counterexample. For almost the simplest possible nontrivial example, you could try f(t) = sin(t) + 1, g(t) = f(t) * f(t). - Tim
From: William Elliot on 6 Jun 2010 04:56 On Sat, 6 Jun 2010, Tim Little wrote: > On 2010-06-06, Bret Cahill <BretCahill(a)peoplepc.com> wrote: >> Several functions in an equation have ac and dc components. If all >> the dc is filtered out of the functions for ac only and then all the >> ac out of the dc, will the equation hold for just the dc and just >> the ac? >> >> The equation doesn't do anything more than add, multiply and divide >> the functions. > > No. Almost any nontrivial set of functions and equations would > provide a counterexample. > > For almost the simplest possible nontrivial example, you could try > f(t) = sin(t) + 1, g(t) = f(t) * f(t). > As g(t) = sin^2 t + 2.sin t + 1, I'd say he's correct.
From: mecej4 on 6 Jun 2010 08:07 Bret Cahill wrote: > Several functions in an equation have ac and dc components. If all > the dc is filtered out of the functions for ac only and then all the > ac out of the dc, will the equation hold for just the dc and just the > ac? > > The equation doesn't do anything more than add, multiply and divide > the functions. > > > Bret Cahill Consider sin t + cos t = (\sqrt 2) sin (t + Pi / 4) as a test case. -- mecej4
From: hagman on 6 Jun 2010 09:45
On 6 Jun., 10:56, William Elliot <ma...(a)rdrop.remove.com> wrote: > On Sat, 6 Jun 2010, Tim Little wrote: > > On 2010-06-06, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > >> Several functions in an equation have ac and dc components. If all > >> the dc is filtered out of the functions for ac only and then all the > >> ac out of the dc, will the equation hold for just the dc and just > >> the ac? > > >> The equation doesn't do anything more than add, multiply and divide > >> the functions. > > > No. Almost any nontrivial set of functions and equations would > > provide a counterexample. > > > For almost the simplest possible nontrivial example, you could try > > f(t) = sin(t) + 1, g(t) = f(t) * f(t). > > As > g(t) = sin^2 t + 2.sin t + 1, > I'd say he's correct. I won't. "AC" part of f is sin(t), AC part of g is sin^2 t + 2.sin t-1/2, which is not the square of sin(t). DC part of f is 1, DC part of g is 3/2, which is not the square of 1. |