# Voss algorithm and pink noise

the voss' algorithm generated a 1/f series. What does the series mean? For example, we use three dice and the result sequence length is 8. Let's set the sequence is 8,15,6,9,14,10,9,7. Then what does this sequence mean? does it mean the sequence of frequency or something else?

## 1 Answer

The sequence produced by the Voss algorithm is a sequence of random numbers whose power spectral density decays with frequency as $1/f$. In other words, if you find the magnitude spectrum of the sequence (in other words, the magnitude of the DFT of the sequence), you'll see that it decays roughtly as $1/f$.

As to the meaning of the sequence: it doesn't have any intrisic meaning. One way to think about it is as noise with a particular frequency spectrum. In other words, if you normalize the sequence and feed it to your sound card, you'll hear a certain kind of noise. This noise can be added to other signals, such as audio, to give it specific properties.

If all you need is $1/$ noise, there are other methods to generate it; see Pink ($1/f$) pseudo-random noise generation.

• So I set a frequency(let's say F0) of the sequence of random numbers. Then I use the frequency F0 and the sequence numbers to generate a power spectral density. Then the generated power spectral density decays will be 1/F0? Am I correct? – NHa Nov 4 '15 at 22:47
• And there is another question. If the length of sequence of random numbers is 8 like above and the frequency is 44100hz. Then how to get the frequency spectrum? – NHa Nov 4 '15 at 22:58
• You use the DFT. If the sequence has $N$ numbers, you get $N$ "bins". If the sequence corresponds to noise sampled at frequency $f_s$, each bin corresponds to frequency $f_s/N$. In every case, you'll get similar behavior of the PSD. This is a bit off-topic for this question -- if you need more help on the DFT, I suggest you start by reading some of the many DFT-related answers on this site. – MBaz Nov 4 '15 at 23:07