[sdiy] Additive Synthesis - phase shifts important??

[cheater cheater]

Guys,

there are several misconceptions here that need to be cleared up:

1. what is phase shift?
there are several things that go under the general term phase shift
that are *very* different.

a) phase shift of a complete signal by time. This is the incorrect
name and it should be 'delay by time'. Given that there is only one
signal and the phase shift is constant, it can be any arbitrary value
and you won't be able to notice the delay on its own. If the delay's
derivative is non-zero, this can be noticed as pitch bending (think
chorus etc). If the delay's derivative is constant and non-zero, the
pitch shift is constant.

b) phase shift of a subsignal by time. This is the incorrect name and
it should be '(micro)delay by time'. this can be noticed, e.g. take
two saw signals and invert them. They will cancel out. If you shift
one of them, you will get a rectangle wave. By changing the microdelay
you change the pulse width.

c) phase shift of a signal by angle. Sometimes called group delay.
This is the most important one and most difficult to understand for
most people. That's what is sometimes shown on speaker specification
sheets, filter measurement sheets, etc. It's a value expressed in
multiples of Pi and usually wrapped to be in the interval [0, 2Pi) or
the interval (-Pi, Pi].

c) varies vastly from a) and b) as it's not a value that expresses a
concept natural to the time domain form of a signal, but instead the
frequency domain form of a signal.
What happens if you shift a signal's phase by a constant value? For
example, if you shift the phase of a square wave's partials by Pi/2,
you get an 'arc sin' wave. Compare
http://www.audioxpress.com/magsdirx/ax/addenda/media/colin2842.pdf fig
6. This was, by the way, written by one of the guys who made the Arp
2600.

The key to understanding this is that the value is expressed in units
relative to the frequency of the partial the shifting of we're talking
about. So, for one partial, Pi/2 might be 0.4995ms, for another it
could be 0.755(2)ms. This gives you very unexpected results,
especially if you have non-harmonic partials.

For small values, the phase shift just 'sweetens up' the sound. It can
lessen the attacks and make the sound more pleasant to the ear, sort
of like a tiny amount of chorus added, but not. This effect is used by
some mixing engineers who simply put their mixes through EQs set to
flat. The EQs still have built-in group delay makeup which does affect
the sound no matter what you do. This also happens in all those
vintage transformers etc.

For high values, you can get very drastic differences, also in timbre.

There's a tabu about never equalizing a Stradivarius. And this is very
true, as most EQs will change the phase relations of the harmonics of
the sound - which is the reason why a Stradivarius sounds like one in
the first place.

So the actual phase shift (the real 'phase shift', not microdelays)
does not have to vary to be noticeable.

d) phase reverse. If you shift the phase (in the definition of c)) by
1Pi, you get an inverse of the signal. Cool, huh?

One thing some might not realize is that phase shift, unless done in a
band-limited fashion, is an infinite-response tool: you can always go
an octave lower, and then the phase shift for that harmonic will be
twice as long as for the previous one.

2. Negative frequencies.

Every physics teacher would (and should) paddle your ass for saying
this :) A frequency cannot be negative. This is a 'term'/'catchphrase'
populated by people reading FM-design books which were written by
other people who didn't care enough.
What people usually refer to here is a negative first derivative of
the phase driver.
A frequency is defined as a number which indicates the amount of
events that have happened in the duration of a SI second, and is
counted with the unit Hertz. As much as events cannot 'unhappen', the
amount of those events cannot be negative, and thus a frequency cannot
be negative. That's simple math - I hope! :)

Remember: being an engineer doesn't let you bend the laws of physics or maths.
If you're trying to do so, you're probably expressing yourself in a
way which will create errors in later reasoning. And thus, your work
becomes pointless.

I'm not ranting at any people on this list - just reminding of what
can happen if your engineering work slides to the 'lyrical' side of
things, rather than the 'technical' :)

Then again, granted, there are some impressive mistakes in
non-academic pseudoscience which yielded very interesting and useful
results. Like rock music. 8)

Cheers

On 7/14/08, Florian Anwander <Florian.Anwander at consol.de> wrote:
> Hi Florian,
>
>  It makes a huge difference for attack-phase of percussive sounds: does the
> wave start with the most possible peak or not.
>
>  Also it will be relevant if you use two additive oscillators and one hase
> phase shifted harmonics and the other oscillator doesn't.
>
>  Florian (sic!)
>
>
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