[sdiy] A question about phasers/notch filters

[ASSI]

On Saturday 08 October 2011, Tom Wiltshire wrote:
> There are some things I don't understand about the frequency shifting
> method. I think I understand the frequency shifting itself. You take a
> frequency A, ring mod it with a signal B, which gives you frequencies
> A+B and A-B. If you simultaneously ring modulate A with a shifted
> version of B, you can presumably cancel either A-B or A+B to leave you
> with just the 'single sideband' you mentioned. Is that right?

The answer is probably "no", but maybe I just don't understand what you're 
meant to say.  Before I wreck the explanation myself, here's J. O. Smith to 
the rescue:

https://ccrma.stanford.edu/~jos/st/Analytic_Signals_Hilbert_Transform.html

So, the whole point of the exercise is that only one of the sidebands is 
produced if you are mixing analytical (or quadrature) signals.  In reality 
you will always have some leakage into the other sideband since a Hilbert 
Transformer (filter with a constant phase shift of 90° for all frequencies) 
isn't realizable for arbitrary signals.

> The bit I don't get is why adding that shifted signal back to the
> original would give *moving* notches. I suppose it's to do with the beat
> frequencies between the two signals, in the same way that two close
> frequencies sound like one frequency modulated by an LFO (which isn't
> really there). I'll have to think about that a bit more until it becomes
> clearer.

Richie Burnett already answered that question briefly in response to how the 
Buchla 297 might work.  Frequency is a measure of how fast the (unwrapped) 
phase changes, so a constant frequency difference between two signals 
imparts a linearly increasing phase shift (aka delay) between them.  Mapped 
back to the concept of a traditional phaser that means you'd need to 
implement notches that continually move to infinity and you'd have to 
implement an infinite number of them.  That of course isn't realizable, 
which is exactly why in a traditional phaser you will have to reverse the 
direction of modulation at some point.


HTH,
Achim.
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