Re: harmonic extraction

["reinifrosch@xxxxxxxxxx" <reinifrosch@xxxxxxxxxx>]

David,

A few hours ago, I reacted to the last sentence of your message. 
Now I would like to comment on the remainder. I seem to
disagree with (or to misunderstand) your second sentence
("Still, absorption losses ... even harmonic signatures"). 

A square wave having odd symmetry with respect to the time 
origin has the following Fourier transform:

x(t) = sin(om t) + (1/3) sin(3om t) + (1/5) sin(5om t) + ... ,

where om = omega = 2pi f. 

A square wave having even symmetry with respect to the time 
origin has the following Fourier transform:

x(t) = cos(om t) - (1/3) cos(3om t) + (1/5) cos(5om t) - ... .

In both cases, there are ODD harmonics only.

Reinhart.

----Ursprüngliche Nachricht----------------------------
Von: smithd@xxxxxxxx
Datum: 27.03.2009 18:26
An: <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: harmonic extraction

Jim,

I was afraid of that.

Still, absorbtion losses for complex waveforms should always produce
something more closely approximating a square wave, ie even harmonic
signatures.   This leads me to ask if we ever "hear" a pure sin wave. 
Perhaps this is why signals with odd harmonics have that hollow
dissonant quality?

Dave

----- Original Message -----
From: "James Bashford"
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: [AUDITORY] harmonic extraction
Date: Fri, 27 Mar 2009 11:56:34 -0500

David,

The stimuli I'm working with have a different, randomly
determined starting phase for each harmonic, and all 
harmonics are matched in level.

Jim
----------------------------------------------------------
Reinhart Frosch,
Dr. phil. nat.,
r. PSI and ETH Zurich,
Sommerhaldenstr. 5B,
CH-5200 Brugg.
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .