Jörn Nettingsmeier nettings at folkwang-hochschule.de
Sat Jun 25 22:22:58 UTC 2011

```On 06/26/2011 12:04 AM, Emanuel Rumpf wrote:
> 2011/6/25 Fons Adriaensen<fons at linuxaudio.org>:
>> 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.

```