[sdiy] More infinite-phasing examples

[Richie Burnett]

> Richie: how many notches are in the audio range at any one time ?
> Can the number of notches be increased. If they could be increased,
> would the resultant sound have more of an effect, or would the
> overall effect be less dramatic ?

The first clip: http://www.richieburnett.co.uk/temp/audio_phased1.mp3
has 2 or 3 notches between 20Hz and 20kHz.  They are spaced non-harmonically and
sweep upwards exponentially (i.e. linear in octaves).  A new notch enters the
bottom of the audio range just before the top one goes above 20kHz.

The second clip: http://www.richieburnett.co.uk/temp/audio_phased2.mp3
has 8 notches in the audio band at any time.  These are almost spaced
harmonically (regular kHz intervals) and sweep downwards linearly in frequency.

If you can view a spectrogram of the audio file in your favourite wave editor as
it plays then the second audio example yields something that looks very much
like a barber pole.  (The notches are clearly visible in a spectrum graph too if
that's an option.)

You can have any number of notches you want.  It just depends how much phase
shift or delay you introduce into one of the paths before mixing the dry and
frequency-shifted versions back together.  In the first example I used only the
phase-shift from the Hilbert transformer in the frequency-shifter itself and
that tends to give few notches spaced widely over octaves of audio spectrum.  In
the second example I introduced a pure delay into the dry signal because it's
trivial to do digitially.  This yields a whole bunch of notches regularly spaced
in frequency, more reminiscent of a chorus or flanger than a phaser.  I only
used a delay of a dozen or so samples (about 250us I think.)  Long delays can
easily yield thousands of moving notches.

Different numbers of notches definitely have different sounds, as do linearly
spaced vs exponentially spaced notches.  Fortunately it's quite easy to play
about with these and evaluate the options.

> It would be really complex, but maybe not any more complex than the
> frequency shifted method...

The frequency shifted method isn't really that complicated digitally.  The
problem with an analogue solution is the amount of circuitry involved and all
the component tolerances in the allpass networks.  Less-than-ideal performance
in the four-quadrant multipliers also impacts the performance of an analogue
frequency-shifter heavily.

-Richie,