[sdiy] A different approach to frequency shifting?

[jhaible]

This is how I understand it: You're making an ordinary RM with a carrier
so high that both sidebands are not folding back along zero. (Stage 1)
Then you can get rid of the unwanted sideband by "simple" (see below)
filtering. (Stage 2). Then you could use another RM to modulate the
remaining sideband back down to the audio range (Satge 3). But
alas, here (3) you would produce 2 sidebands again.
This is overcome by using *two* stages (1) and (2) each, with a quadrature
carrier. Then, after the two stages (2) you have a quadrature audio
signal, just located too high in the frequency range. This can be
Frequency-shifted down (with 2 RMs and a quadrature carrier)
just like an ordinary (not previously up-shifted) quadrature audio signal.

So the stages (1) and (2) are merely a different way to produce
a quadrature audio signal (instead of using a dome filter). That this
quadrature audio signal is not in the baseband anymore, is just a
minor detail, as we're performing a "real" quadrature FS operation
afterwards anyway (Stage 3).

Now where is the catch?
I think the "simple filters" must actually be rather steep. By pre-shifting
the
audio material up into higher regions you get the opportunity to use
a simple *filter* to get rid of unwanted sidebands in the first place;
but this upshift also means that the 20 or 50Hz or whatever you
calculate for the range between passband and stopband get very
small *relative* to the high frequency range you're now working in.

So I guess you'd need a filter of very high order (and of course two
such filters with exact matching). Which asks for a digital, not
an analogue, soulution IMO.

I may be wrong in overestimating the demand on the filter slopes
(Maybe there is some other helpful cancellation going on here?),
but this is how I interpret it after a first glance (and with very
vague memories on signal theory lessons).

JH.



> I remember that this one was an exercise in my communication theory
> courses on university. Just a feeling: suspiciously simple, too simple.
> I did not do the math yet.
> I mean the task to get rid of one sideband is not at all simple.
> This article suggests  that it would be simple (no special requirement
> for the LP filters).
> Smells like nonsense, but I could be wrong.
>
> For analog implementations the scheme suffers from that
> the input is not necessarily band limited, i.e. the folded
> sideband can possibly creap up into the other sideband
> area. This can of course be excluded in a sampling system.
>
> m.c.
>
> -----Original Message-----
> From: Thomas Hudson [mailto:thomas_hudson at mac.com]
> Sent: Donnerstag, 24. April 2003 21:29
> To: synth-diy at dropmix.xs4all.nl
> Subject: [sdiy] A different approach to frequency shifting?
>
>
>
> I came across an article in CSound Magazine from Summer 2000 about an
approach to frequency shifting I hadn't seen before. It uses a quadrature
oscillator and two multipliers followed by two LP filters and then another
quadrature oscillator and pair of multipliers. The difference in frequency
between the two oscillators determines the shift:
>
> http://www.csounds.com/ezine/summer2000/processing/index.html
>
> It seems that this method would be simplest for thru-zero effects. The
article is in the context of a digital implementation, but has anyone used
this technique in the analog world?
>
> TH
>
>
>