[sdiy] Phase shifts and instantaneous frequency

[Aaron Lanterman]

On Jul 15, 2008, at 7:07 PM, Ian Fritz wrote:

> At 04:47 PM 7/15/2008, Aaron Lanterman wrote:
>
>> If I imagine that somewhere in my auditory system, a 100 Hz wave  
>> and a
>> 201 Hz wave are being multiplied, then I get sum and difference tones
>> of 301 Hz and 1 Hz.
>
> ???? ... I get 201-100 = 101 and 201+100 = 301.  How do you get 1 Hz?

Oh, that would be me totally smoking crack. Scratch that crack-laden  
paragraph of mine.

> The 1 Hz modulation comes from beating of the 101 Hz and 100 Hz  
> signals.

That might be the case, but the perceived beat seems to be more easily  
explained by simply noting it's a wave that's periodic with a period  
of 1 Hz. There might be weird complicated intermodulations going on in  
the ear, but we don't _have_ to fully resort to them to explain what's  
happening in that particular example. You can see it in the waveform  
without having to invoke any notes about what's happening in the ear.

> I have read that the nonlinearity in the ear is simply the asymmety  
> in the eardrum.

I should ping my colleagues about this (we've got a strong audio/ 
speech processing group here), it might be interesting to see what  
they have to say.

- Aaron