Subject: Re: harmonic extraction From: "reinifrosch@xxxxxxxx" <reinifrosch@xxxxxxxx> Date: Tue, 31 Mar 2009 15:01:58 +0000 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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@xxxxxxxx> 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@xxxxxxxx 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@xxxxxxxx .