It sounds like this“An equaliser or any filter changes a sound by adding new frequencies that weren't there.”
Thinking an equaliser adds new notes
Why it feels right
A filter changes how a sound sounds, and sometimes dramatically: a telephone voice, a muffled voice behind a wall, a bass boost. When the character changes that much, it seems that something new has to be created, not just taken away.
Why it’s wrong
A linear filter, such as an equaliser, a speaker or a room, can only change the strength and timing of the frequencies already present. A pure 100 Hz tone goes in and a 100 Hz tone comes out, maybe quieter or delayed. New frequencies appear only with distortion, which isn't linear.
A worked example
Most of the things that shape sound, such as a room, a speaker cabinet, a tone control, are close to linear and time-invariant: double the input and the output doubles; a delayed input gives a delayed output. For such a system, a sine wave in gives a sine wave of the same frequency out, scaled and shifted in time. It cannot turn 100 Hz into 300 Hz.
That makes the analysis easy. Split the input into its frequencies. Each is multiplied by a number, the filter's gain at that frequency, and shifted by a phase. Add them back up. A telephone line works by scaling down everything below 300 Hz and above 3,400 Hz, to almost nothing. Nothing is added.
New frequencies come from non-linear things, such as an overdriven guitar amplifier that clips the peaks off the wave. Clipping a 100 Hz sine makes it more like a square wave, which adds harmonics at 300, 500 Hz and so on. That is distortion, and it is what separates a clean equaliser from a fuzz pedal.
How to catch yourself
- You say a filter 'adds' frequencies.
- You can't say why a clean equaliser can't add a note.
- You mix up filtering with distortion.
What to hold instead
For a linear system such as an equaliser, a sine in gives a sine of the same frequency out, changed in size and timing. It can only reshape what's there. New frequencies come from distortion, which is non-linear.
Where you’ll meet it
- Using an equaliser on a recording.
- Wondering why a telephone voice sounds thin.
- Telling clean boost from overdrive.
Questions people ask
- Can a filter create frequencies that weren't in the signal?
- Not if it is linear. A linear filter only scales and shifts the frequencies already present. Creating new ones needs a non-linear effect such as clipping or distortion.
- Why are sine waves special for filters?
- Because a sine through a linear, time-invariant system comes out as a sine of the same frequency. That lets you handle each frequency separately, which is why the Fourier transform makes filter design much simpler.