What digital sound actually is

Sound is wiggling air

When something makes a sound — a voice, a guitar string, a slammed door — it pushes the air next to it, which pushes the air next to that, and so on, until a little wave of pressure reaches your eardrum and wiggles it. Your brain reads that wiggle as sound. That’s all sound is: changing air pressure over time.

If you could draw the pressure at your ear from one moment to the next, you’d get a wavy line: up when the air is squeezed, down when it’s thinned out. That wavy line is called a waveform, and it’s the single most important picture in this whole book. Loud sounds make tall wiggles; quiet sounds make small ones. Fast wiggles are high-pitched; slow wiggles are low-pitched.

Turning the wiggle into numbers

A computer can’t store a smooth wiggly line directly. Instead it does something clever and slightly brutal: many thousands of times per second, it measures how high the wave is right now and writes that height down as a number. Then it throws away everything in between.

Each measurement is called a sample. Think of it like a flipbook: a cartoon isn’t really moving, it’s just a stack of still drawings shown fast enough to fool your eye. Digital audio is the same trick for sound — a stack of still “heights,” played back fast enough to fool your ear.

 height
  +1 ┤        ●                 ●                          loud  = tall wiggles
     │     ●     ●           ●     ●                        quiet = small wiggles
   0 ┼──●───────────●─────●───────────●─────────►  time    fast  = high pitch
     │                 ●                   ●               slow  = low pitch
  -1 ┤                    ●  ●         ●
       └ each ● is ONE sample: a single measured height.
         Join the dots and you get the "waveform".

Two numbers describe how finely the computer captured the sound:

• Sample rate — how many measurements per second. CD audio uses 44,100 per second (written 44.1 kHz); video and pro audio often use 48,000. The more samples per second, the higher the pitches you can capture. (There’s a famous rule: to capture a pitch, you need at least twice as many samples per second as the pitch’s frequency. We’ll meet it again in the resampling chapter.)
• Bit depth — how finely each single measurement is written down: 16 bits per sample for CDs, 24 bits for studios. More bits means a quieter “noise floor” — the faint background fuzz that any digital measurement carries.

Inside cathar (and most modern tools), every sample is stored as a floating- point number between −1.0 and +1.0. −1.0 is the lowest the wave can go, +1.0 the highest, and 0.0 is silence (no pressure change). A whole second of mono CD audio is therefore just a list of 44,100 such numbers. A stereo recording is two such lists, one for the left ear and one for the right.

Why this matters for cleaning up sound

Every restoration tool in this book is, underneath, just arithmetic on that list of numbers. Removing hiss means nudging the numbers; removing a click means replacing a few of them; making something louder means multiplying them all. There is nothing else in the file. When cathar “denoises an interview,” it reads the list, does sums on it, and writes a new list. The art is entirely in which sums, and why.

There is a catch, though, and it sends us straight to the next chapter. Looking at the raw list of heights — the waveform — is a great way to see how loud something is from moment to moment, but a terrible way to see what’s in it. A hiss and a voice and a hum are all jumbled together in the same wiggly line, like three colours of paint stirred into one bucket. To pull them apart, we need a second way of looking at sound.