[PD] Negative frequency of modulating sinusouid in FT

Maximiliano Estudies maxiestudies at gmail.com
Thu Jul 30 11:59:59 CEST 2020

```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 at ucsd.edu>)
escribiÃ³:

> 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
>
> > _______________________________________________
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>

--
Maximiliano Estudies
*VDT Referat Beschallung*
+49 176 36784771
omslo.com
maxiestudies.com
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