Null testing

Every sample is just a number#

A WAV file stores a sequence of level values and a little metadata at the start: sample rate, bit depth, channel count. That's it. It says nothing explicit about frequency, transients or harmonics. Those are implicit, and you have to derive them, for example with an FFT.

So gain is the most fundamental building block of signal processing. A fader is gain. Compression is gain across time. EQ is gain across frequency. Distortion is gain that depends on the level going in. If you change the gain of individual samples, you haven't changed "just the level". You can change anything. In one video I added the right per-sample changes to a horrible MP3 of telephone hold music and got an orchestral recording of Mozart.

The delta is the whole story#

Hold music minus Mozart equals the delta. Rearrange it and Mozart plus the delta equals the hold music. To get the delta between any two signals, you flip the polarity of one and sum them, and what's left is the difference.

People say the delta "doesn't tell the whole story". Wrong. Digital audio is nothing but level values, so A minus B is the complete difference, and there is no other information it could be missing. Any harmonics, saturation, "vibe" or frequency dependence in a processor has to show up in it. What is true is that a delta can be accurate without being human-comprehensible. If it just looks fuzzy, you need other tools to find out what the fuzziness is: listen to it, put it through a frequency and phase analyser, look at the harmonics. It might be nothing more than a non-linear-phase anti-aliasing filter that sounds identical.

A null does not have to reach minus infinity#

A null at minus infinity means the two signals are mathematically identical. The question is whether what's left is audible, and that has to be scaled against hearing, in the context of the music.

You can often hear a delta when it's soloed and turned up, even though the change it represents, say 0.1 dB, is inaudible in the mix.

An inaudible delta means no difference#

Saying "the delta is practically inaudible but I can still feel the difference" puts feelings above measurement. People can argue that on the internet if they like.

The same goes for "legendary" vintage gear. Calling something magic without being able to explain it in maths or physics isn't an explanation.

Dynamics need the delta over time#

A compressor's transfer-function chart shows where the level ends up, not how it gets there. It could go down in a straight line, a convex curve, a concave curve or a zigzag. Without time, a compressor, limiter, gate or expander is just a waveshaper. That's why I built Delta Expose: it plots the sample-by-sample delta over time and shows the gain-reduction curve directly.

Convexity has the same view built into each instance.