Small Phase Angle Between Two Functions
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From: Bret Cahill on 10 Aug 2010 10:25 Two functions, sin(x) and sin(x + phi), are separated by a small phase angle. The different between the functions, sin(x) - sin(x + phi) can be approximated by phi times the derivative of sin(x) = phi cos(x). Will this work for all waveforms separated by a small phase angle? Bret Cahill
From: Narasimham on 10 Aug 2010 16:40 On Aug 10, 7:25 pm, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > Two functions, sin(x) and sin(x + phi), are separated by a small phase > angle. > > The different between the functions, sin(x) - sin(x + phi) can be > approximated by phi times the derivative of sin(x) = phi cos(x). The difference between the functions, sin(x) - sin(x - phi) can be approximated by phi times the derivative of sin(x) = phi cos(x). > Will this work for all waveforms separated by a small phase angle? > > Bret Cahill Yes, phi f'(x). that is the definition of derivative. Narasimham
From: Tim Little on 10 Aug 2010 21:01 On 2010-08-10, Bret Cahill <BretCahill(a)peoplepc.com> wrote: > The different between the functions, sin(x) - sin(x + phi) can be > approximated by phi times the derivative of sin(x) = phi cos(x). > > Will this work for all waveforms separated by a small phase angle? If the waveform is differentiable, yes. That property (when formalized) is actually the definition of the derivative. - Tim
From: Bret Cahill on 11 Aug 2010 10:00
Thanks. Bret Cahill |