How to generate colored noise?

I'm trying to reproduce a sound effect, and spectrum analysis of the effect shows long vertical bars at regular intervals. Said vertical bars indicate that many fequencies are being played simultaneously.

At first I suspected that I might be able to reproduce this effect by using a square wave, triangle wave, or sawtooth wave, as I knew that these had all sorts of harmonics in them. However, when I tested this hypothesis in sound forge by geerating said waves and then analyzing them, I found the results weren't at all similar to what I had in my sound effect.

So I'm thinking I need some way to generate colored noise, perhaps by altering white noise using some kind of graphic equalizer and retaining only those frequencies in a specific range.

Anyone have any suggestions in regards to this? I guess my next step is to test that method involving the graphic equalizer, as that just occured to me now.

But even if that works, I would still either need a way to perform that operation in the Arduino, or store a sample of some length that I could play back. I think I would rather simply calculate the data in code when my program starts.

After some research into graphic equalization I came upon parametric equalization and while investigating sound forge's parametric equalizer I noticed the band pass filter.

I now think what I am looking for here is code for a bandpass filter, to which I would pass white noise.