Digital noise generation can easily be done with LFSR-registers as well as in hardware and as in software. This article shows, how to shape the spectrum accordingly to your needs:

A logic circuit represents a 20-bit LFSR that implements the well-established primitive polynom x^20 + x^3 + 1. It consists of 20 D-flip-flops connected in series, all connected to the same clock source. The output of bit 20 is fed directly back into the D input of bit 1.
An XOR gate is located between bit 3 and bit 4: It combines the output of bit 3 with the feedback signal from bit 20, and the result is fed into the input of bit 4. That already creates a suitable noise. The resulting frequency spacing is less than 0.1 Hz and thus completely inaudible for the ear. It is a uniform, analog hissing sound (close to white noise) with no defined pitch.

Using modern programable PLDs they are easy to be realized.