Brown noise is a type of noise similar to white noise, but rather than having an equal representation of all frequencies, the lower frequencies are represented more than the higher ones. This results in brown noise being much more pleasant to the ear.

Natural sources of brown noise include waves breaking on a shore, wind blowing past your ear, and so on. White noise may have equal representation across the spectrum, but due to the way the ear perceives sound, the high frequencies seem to be much louder.

One interesting thing about brown noise is that it's easier for you to imagine sounds in your head when listening to it, because your ears are receiving neutral stimuli and the brain can pick up what it wants from the palette.

### What is brown noise?

Brown noise is noise that falls off at -6 dB per octave, that is, noise whose amplitude at a given frequency is inversely proportional to the frequency. Amplitude is the square of power, and the power of brown noise at any given frequency is inversely proportional to the square of the frequency. Thus, brown noise is to pink noise as pink noise is to white noise.

### But why is it called "brown" noise?

Brown noise is named after Dr. Robert Brown (no relation to Bobby Brown), who first described Brownian motion. The displacement of a particle undergoing Brownian motion is a source of brown noise.

### How can I generate brown noise?

If you have white noise, possibly from a thermal noise source, integrate the white noise with respect to time. The integral operator is an IIR filter, whose impulse response is the Heaviside function, that introduces the desired -6 dB/octave rolloff. You'll want to saturate (clip) the output so that extremely low frequencies don't cause annoying wrap-around distortion.

### Once I have brown noise, what can I do with it?

To get white noise from brown noise, take the derivative (an FIR filter).

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