[sdiy] Different pole notches and phasers

[Richie Burnett]

>> In the simplest instance, if you take a signal, delay it and mix it back 
>> in
>>with the original, you will get notches.  This is the classic comb filter.
>
>In this case, are the notches distributed evenly? Is the space between each 
>notch determined by the delay time?

Yes,  There is a notch at every frequency where the delay line contributes 
an odd multiple of 180 degrees of phase shift, so that you get destructive 
interference when you mix it with the raw input signal.

> What sort of db/oct gain do we see?

There isn't any roll-off. Pure delay is an all pass filter.

> In the classic 4pole cascaded OTA phaser design, my ears tell me there is 
> only one notch, but I'm not sure I'm hearing it right.

I think there is more than one notch, and they won't be harmonically related 
like they are in a flanger.

> Looking at figure ten in http://soundsemiconductor.com/downloads/AN701.pdf 
> I see that a one-pole allpass gives you 180degree phase rotation around 
> the cutoff.

The best way to think of a single 1st order phase-shifter stage is to think 
of it as a 1st order lowpass filter with a gain of 2, and a direct path gain 
of -1.  Then think of what the output would be below the cutoff frequency, 
at the cutoff frequency and then above the cutoff frequency.  If you can, 
plot it on a Nyquist plot.  You get a semicircle centered on the origin 
confirming that you get 180deg of phase shift from low freq to high freq, 
and the amplitude is constant.

> So I suppose if we have two of them, then we get 360degree phase shift. As 
> we add more poles, and increase that phase shift, doesn't that start 
> looking more like delay? Does that mean we get classic comb filtering 
> effects, ie a spread of notches above the APF's cutoff? Am I making any 
> sense?

The more stages you add, the more phase shift you get across the audio band, 
and the more places you potentially get destructive interference.  The 
frequencies of the notches aren't naturally harmonically related though. 
That's why a phaser sounds different to a flanger.

-Richie,