[notfashion]

If I understand this correctly, it's not even a matter of using a filter, just a case of summing some random sinusoids with an appropriate weighting for each according to the frequency. You can do this by starting off with noise in the frequency domain and shaping it before doing an iFFT.

[enriquto]

Yes, I meant exactly that. You build a spectrum by setting the amplitudes to the desired decay law, and the phases to random. It is an octave/matlab one-liner.