# White noise at non integer intervals, bug or my mistake?

I'm intending to add white noise to a simple periodic signal

   p = TransformedProcess[
Cos[t/8] + noise[t],
noise \[Distributed] WhiteNoiseProcess[],
t];


Adding it at integer intervals is fine

   data = RandomFunction[p, {0, 10}]


yields a TemporalData value as expected

But

   data = RandomFunction[p, {0, 10, 0.1}]


causes an error

"The specification WhiteNoiseProcess[NormalDistribution[0,1]] is not a random process recognized by the system"

Am I at fault or is it a bug?

## 1 Answer

The issue is to do with RandomFunction

For continuous-time processes with jumps, such as WhiteNoiseProcess[] the step dt is random and given by the process itself.

e.g this works

RandomFunction[WhiteNoiseProcess[1/3], {0, 50}]


This doesn't

RandomFunction[WhiteNoiseProcess[1/3], {0, 50,0.1}]


For continuous-time processes without jumps, such as WienerProcess an explicit dt needs to be given.

e.g this works

RandomFunction[WienerProcess[], {0, 50, 0.1}]


this doesn't

RandomFunction[WienerProcess[], {0, 50}]


You can't mix the two.

• thanks, that with reference.wolfram.com/language/ref/TimeSeriesRescale.html will meet my needs. Just makes me ponder about the real nature of white noise. Is there a better solution to modelling acoustic noise than white noise? The time series I’m modelling in the end being an acoustic one. – Nick Jan 2 '20 at 18:47