or: The Babylonian DSP Confusion

If I place myself in front of my car and bang hard with a hammer on its body, I will in all likelihood create a dent. However, if I go inside the car and bang from there on the car body, then I create – observed from the outside – a bump. (By the way, it also functions with other people’s cars. Every body shop man knows that).
Do we now have to differentiate between a 'dent hammer' and a 'bump hammer' in order to understand the phenomenon?
Hardly likely: The tool is, in any case, purely and simply a hammer; the rest is a matter of perspective. Strictly speaking, two perspectives: that of the application and that of the effect.

As preposterous as this example may also seem, I take it as a simile for the confusion of terms in the world of digital signal processing and the audio effects that we deal with daily.
Certainly, the perspectives are somewhat more complicated, not simply 'inside' or 'outside',
to be changed by a body movement. In essence, however, it is always a matter of a perspective in which one causes something – and another perspective from which one can judge the effect.
Ouch, if that is not clear in the communication! Then the
'pitch-phase-time-shift-stretch-spec-confusion' is perfect.

For me, it is not so much a matter of the way things are designated. If one invents or discovers something, then one has to somehow name it if one would like to discuss it with others. Not always are such initial designations that are adopted by the experts fortunate.
[One only has to think about the 'imaginary numbers'. C.F.Gauss was of the opinion that the complexes and imaginary numbers are so hard for many people to understand only because they are named so unfortunately!]. Often they are also non-uniform.
Much more important than that is, however, what they refer to. Will a tool be designated, a process named or a phenomenon of its effect from some perspective or another?
In the second case, it will become difficult if we occasionally want to change the perspective. Then we would actually need an own name for the same thing in every perspective (level or domain) – already a balancing act with only two levels; and an impossible thing when there are several.
And the large contexts that we use compositionally and through which we could advance to new, aesthetic consequences slip away from us!

An example: filter.
Everyone who deals with electroacoustics or communications engineering knows more or less what a filter is.
What happens, however, if I apply a filter in the spectrum? – Stop! No! – I don
't mean: What do I have to do in the spectrum so that something like filtering takes place in the time perspective? I mean: What effect does it have if I apply this routine, which is called filtering in a time context, in the spectrum?
The effect is an envelope modulation, it's clear. In VASP:

sfload anysound.wav
lp2 500hz

A lowpass of quality q=2 with a cutoff frequency of 500 Hz. (It is, however, my steady-state filter, in case it is not denoted differently, and at q=2 one has an edge steepness of 24 dB/octave).
And now this way:

sfload anysound.wav
lp2 500hz

(ovp stands for optimize, view and play. FFT is a 'giant' FFT above the whole sound).

And what about a level in between? – A fractional Fourier transformation:

sfload anysound.wav
FRACFT 45deg
lp2 500hz
FRACFT -45deg

(0 degrees would be the original, 90 degrees the giant FFT; 45 degrees lies exactly in between).
[Whoever should work with FRACFT: as a rule-of-thumb, only use half the buffer; even better, a little less. Otherwise, alias phenomena can appear that are endemic somewhere in time and frequency].

* * *

One can practice such changes of perspective.
I am not of the opinion that musicians have to unconditionally deal with mathematics. However, I find that it cannot hurt them. Some things would be easier to communicate.
Besides, the change of perspective is not a mathematical matter. If one once knows that there is a continuous and reversible frequency/time transformation, it is actually compulsory then.
Of course, if one only takes a few steps every day to the nearest tavern and goes back again, then the notion that the Earth is flat entirely suffices. If one wants to go further, one should nevertheless bear in mind that it is a globe. (And if one wants to go even further, one has to perhaps come up with something different again).


(c) Günther Rabl 2010