http://users.wpi.edu/~joausc/T2sounds.wav

This is a sound clip from a game boy game. I'm trying to figure out how I would make these sounds from scratch, but so far I don't have much luck. From the waveform (here's a part of it: http://users.wpi.edu/~joausc/waveform.bmp ) I can see that it's a pulse wave which varies randomly, decaying over time. I've tried creating a signal that oscillates randomly between the values of -1 and +1, but this sounds indistinguishable from white noise. Does anyone know how I could recreate the sounds I linked to above from scratch?

You might start by checking out what was inside the Game Boy APU.
http://en.wikipedia.org/wiki/Game_Boy_Sound_System

You should definitely have a look here:

http://www.zenpho.co.uk/chipwave.shtml

Great old-game chip sounds...

you need to lower the sampling rate.

easily done by:

[inlet~] [slider ] (range 441 -> 44100)
| |
| [phasor~ 4410]
| |
[samphold~]
|
[outlet~]

Yeesh, that's an interesting waveform. Hardoff has it right though, I often use that trick to get interesting NES/C64 type sounds.

I've tried creating a signal that oscillates randomly between the values of -1 and +1, but this sounds indistinguishable from white noise. Does anyone know how I could recreate the sounds I linked to above from scratch?

I think what you're looking at IS the noise function, which seems to be the largest portion of the sample you posted. Perhaps the noise function is just as you described it, a random "flip-flop." The tone is really buried, and may only be implied by "multiplying" the noise. There are many technical sites with quite gory detail on the Audio Processing Units of various Nintendo stuff, why not build an emulator, then mess around?

* CPU: Custom 8-bit Sharp x80 core at 4.19 MHz which is similar to an Intel 8080 in that all of the registers introduced in the Z80 are not present. However, some of the instruction set enhancements from the Z80, particularly bit manipulation, are present. Still other instructions are unique to this particular flavor of x80 CPU. The core also contains integrated sound generation
* RAM: 8 kB internal S-RAM
* Video RAM: 8 kB internal
* ROM: On-CPU-Die 256-byte bootstrap; 256 kb, 512 kb, 1 Mb, 2 Mb, 4 Mb and 8 Mb cartridges
* Sound: 2 Square Waves, 1 programmable 32-sample 4-bit PCM Wave, 1 White noise. The unit only has one speaker, but headphones provide stereo sound (for further information, see Game Boy music)
* Display: Reflective LCD 160 × 144 pixels
* Screen size: 66 mm (2.6 in) diagonal
* Color Palette: 4 shades of "gray" (green to (very) dark green)
* Communication: Up to 4 Game Boys can be linked together via serial ports
* Power: 6 V, 0.7 W (4 AA batteries provide ~#5 hours)
* Dimensions: 90 mm(W) × 148 mm(H) × 32 mm(D)/3.5 × 5.8 × 1.3 (in)

Blood and Guts of GBA samplerate:

http://www.pineight.com/gba/samplerates/

Thank you all for your help. The samphold~ thing seems to do the trick, producing a sound that sounds much closer to the clip I posted than white noise. It sounds a little bit shakier than the clip, though, but this is a good start.

@nestor said:

I think what you're looking at IS the noise function, which seems to be the largest portion of the sample you posted. Perhaps the noise function is just as you described it, a random "flip-flop."

Near the end of the clip, there are some noise hi-hat sounds which seem to be actual noise, varying randomly within a range as opposed to most of the sounds which oscillate between two values. It seems strange that sounds in a "noise channel" can either be actual noise or just a random pulse wave. With 44100 Hz white noise I can't tell the difference, though at a lower sampling rate the pulse wave sounds a bit sharper.