On 06/26/2011 12:04 AM, Emanuel Rumpf wrote:
2011/6/25 Fons Adriaensen<[email protected]>:
On Sat, Jun 25, 2011 at 01:55:05PM -0500, Gabriel M. Beddingfield wrote:
Do you mean... for a very simple sine wave?
Assuming yes:
p = asin( x / A )
Where:
A is the amplitude of the sine wave
you mean the maximal amplitude (-MAX<= x<= +MAX) , I guess ?
x is the value of the sample (-A<= x<= A)
p is the phase of the wave in radians (-pi/2<= p<= pi/2)
And what if the phase is< -pi/2 or> +pi/2 ?
since x<= A (always), that result is not possible
?!
it seems you have just proven that the maximum duration of any pure tone
is 1/f. that is quite extraordinary. might it even be the explanation of
the almost mythical 1/f noise? all those tones suddenly realizing they
have to stop or violate rumpf's lemma :-D
sorry, couldn't resist...
but seriously, it does make a lot of sense to talk about arbitrarily
large phase angles. take a look at a real-life speaker system: it's not
uncommon for the HF to lag behind the subs several complete cycles after
passing through the crossover.
even a perfectly phase-linear theoretical speaker exhibits them:
in fact, if you stand 3.4m away from a speaker, the phase angle of a
100hz tone at your ear will be 360° relative to the membrane, while a
200hz tone will be at 720°, and so on.
that's where delay becomes "group delay", i.e. the same constant time
delay implies different phase angles depending on frequency, pretty much
arbitrarily large as the frequency rises.
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