[sdiy] A question about phasers/notch filters

[Richie Burnett]

> I wasn't thinking only of allpass stages though. I understand that you need to
> pile a load of them in series to get the most phase shift you can and generate
> multiple notches. But that isn't the only way to make notches - probably just
> the cheapest/easiest.

You could generate a load of notches using a parallel bank of bandpass filters
and subtracting the outputs of all of the bandpass filters from the dry signal. 
That would give you a whole bunch of notches at the centre frequencies of the
bandpass filters.  This works as a parallel arrangement, but the depth
(attenuation) of the notches is highly dependent on the gain at the peak of each
filter's passband being exactly equal to one.  Something that is hard to
guarantee with real world components in the analogue world, and may be difficult
with coefficient quantisation in the digital world.  You will also get
interaction between the skirts of the bandpass responses when they are close
together which may interfere with the notch depths and shapes.

The neat thing about the cascaded all-pass phaser design is that the frequency
response of the cascaded all-passes is guaranteed to be flat, so the only
adjustment you might need to make is to trim out any gain variations due to
tolerances in the allpass filter's resistor values.  Once this is done, every
notch is guaranteed to be a nice deep one.

> The reason I ask is that I've been reading about the Buchla 297 Infinite phase
> shifter, and wondering how they did the barber's pole phasing.

I'm not familiar with the device you mention, but these "infinitely rising"
barber pole phasing things are usually achieved using a frequency shifter.  If
you can frequency shift a signal using what the radio hams would call
single-sideband supressed-carrier modulation, then you have effectively imparted
a constantly increasing phase shift relative to the original signal.  If you add
this frequency-shifted signal back to the original dry signal I think you get an
infite series of notches that continuously rise or fall in frequency.

Frequency shifting is different from musical pitch shifting and is usually
achieved using a quadrature sinewave oscillator and a pair of ring-modulators
(four-quadrant multipliers).  Since it shifts every spectral component in the
signal by a fixed number of Hz it breaks the harmonic structure of musical
notes.  For this reason it sounds quite discordant for large frequency shifts.

I hope this helps,

-Richie,