26 Jun
2011
26 Jun
'11
12:23 a.m.
On 06/26/2011 12:04 AM, Emanuel Rumpf wrote:
2011/6/25 Fons Adriaensen<fons(a)linuxaudio.org>rg>:
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.
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 ?