[sdiy] A different approach to frequency shifting?

[Magnus Danielson]

From: "Czech Martin" <Martin.Czech at Micronas.com>
Subject: RE: [sdiy] A different approach to frequency shifting?
Date: Fri, 25 Apr 2003 10:54:19 +0200

> 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.

Actually, for me it seems quite simple.

We know we need to have the input signal split into a pair with 90 degrees
phase differance before we mix it with a pair of multipliers and a quadrant
signal. That's in the back-end of this thing. Instead of using a
phase-splitting network it uses the fact that multiplying two sines will cause
addition and subtraction of the angles:

                    AB
Asin(a) * Bsin(b) = -- [cos(a-b) - cos(a+b)]
                    2

Since we do this with a quadrant singal, we let the other quadrant be

c=b+90 deg

(I am actually cheating with propper signs etc, but it doesn't really change
things in this part of the argument)

we get the other output

                    AB                        AB
Asin(a) * Bsin(c) = -- [cos(a-c) - cos(a+c) = -- [cos(a-b-90) - cos(a+b+90)]
                    2                         2

i.e. the other output will have the same properties as the first, but with a
90 degree phase shift.

Since both these signals contains both sum and difference frequencies you need
to single out one of them through filtering, and care must be take to ensure
that these filters have the same phase properties in the passband such that
the relative phase differance remains 90 degrees throughout the usefull
frequency range. The actual phase-responce of the filters is however not very
interesting, just the repeatability of them.

Then the mix-down operates like natural.

I do think that this technique has it's merrits.

I've discovered a good source of polyphase filter material in

http://users.vnet.net/gingell/polyphas/polyphas.html

> 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.

Indeed. If you toss a raw sawtooth, square-wave or pulse you can expect quite
alot of folding products. A lowpass filter at the input to act somewhat of a
anti-aliasing filter would be recommended.

Yeazuz, on all my time here I have not had as much flux in frequency shifter
discussions. Keep the flow up guys!

Cheers,
Magnus