Hey peeps,
I have another question regarding "The Theory and Technique of Electronic Music". It is not directly related to pd, but I guess that many of you will know this stuff and might be able to help me. I hope it is ok. In the last paragraph of 9.1 ( http://msp.ucsd.edu/techniques/latest/book-html/node164.html) the frequency of the modulating signal is defined as having negative frequency (in the book -*kω)*, why is that the case? wouldn't a sinusoid with positive frequency *kω* also give us two partials at 0 and 2*kω*?
Cheers, Maxi
Hi Maxi -
When you modulate a complex sinusoid with another one you only get one sideband, not both. The sideband's frequency is the sum of the two original frequencies - so if they're exact opposites you only get the result at frequency zero.
This is one reason for using complex sinusoids instead of "normal", real-valued ones.
cheers Miller
On Sat, Jul 25, 2020 at 05:44:37PM +0200, Maximiliano Estudies wrote:
Hey peeps,
I have another question regarding "The Theory and Technique of Electronic Music". It is not directly related to pd, but I guess that many of you will know this stuff and might be able to help me. I hope it is ok. In the last paragraph of 9.1 ( http://msp.ucsd.edu/techniques/latest/book-html/node164.html) the frequency of the modulating signal is defined as having negative frequency (in the book -*k??)*, why is that the case? wouldn't a sinusoid with positive frequency *k??* also give us two partials at 0 and 2*k??*?
Cheers, Maxi -- Maximiliano Estudies *VDT Referat Beschallung* +49 176 36784771 omslo.com maxiestudies.com
Pd-list@lists.iem.at mailing list UNSUBSCRIBE and account-management -> https://urldefense.com/v3/__https://lists.puredata.info/listinfo/pd-list__;!...
Hi Miller,
thank you for answering my question. I see it now, it is actually stated a couple of times in the book that when multiplying complex sinusoids their magnitudes multiply and the angular frequency adds, and thus when multiplying a complex sinusoid by a unit magnitude and opposite frequency you get one with the magnitude of the first and zero frequency. Beautiful.
Thank you again for your answer and for the book!
El lun., 27 jul. 2020 a las 19:40, Miller Puckette (msp@ucsd.edu) escribió:
Hi Maxi -
When you modulate a complex sinusoid with another one you only get one sideband, not both. The sideband's frequency is the sum of the two original frequencies - so if they're exact opposites you only get the result at frequency zero.
This is one reason for using complex sinusoids instead of "normal", real-valued ones.
cheers Miller
On Sat, Jul 25, 2020 at 05:44:37PM +0200, Maximiliano Estudies wrote:
Hey peeps,
I have another question regarding "The Theory and Technique of Electronic Music". It is not directly related to pd, but I guess that many of you
will
know this stuff and might be able to help me. I hope it is ok. In the last paragraph of 9.1 ( http://msp.ucsd.edu/techniques/latest/book-html/node164.html) the
frequency
of the modulating signal is defined as having negative frequency (in the book -*k??)*, why is that the case? wouldn't a sinusoid with positive frequency *k??* also give us two partials at 0 and 2*k??*?
Cheers, Maxi -- Maximiliano Estudies *VDT Referat Beschallung* +49 176 36784771 omslo.com maxiestudies.com
Pd-list@lists.iem.at mailing list UNSUBSCRIBE and account-management ->
https://urldefense.com/v3/__https://lists.puredata.info/listinfo/pd-list__;!...
-
Maximiliano Estudies -
Miller Puckette