Dear NG,
I'm looking for a fast way to produce 2d-noise images with 1/f or 1/f^2 spectrum. I currently generate the noise via inverse FFT, but since I need lots of data (~10^7 for a monte carlo simulation) it needs to be really fast. Does someone know a faster way than my approach?
- Dimensionality is between 20x20 and 100x100 - The spectrum doesn't need to be exactly pink/brown, an approximation is fine. - Implementation in either matlab or scientific python (LAPACK anyway)
This is a 1D version that I have using scipy. It's naive, so I'm sure that it is slower. However, I believe the general technique can be implemented on a larger scale.
The basic idea is to sum up a bunch of white time series with different time steps. The first level is white noise at every time step. The second level changes at every second time step. The third changes at every fourth, etc.
I think you can replicate this by generating a few white noise arrays of the appropriate sizes, judiciously using repeat(), and summing them together. I got this scheme from an article I found by googling for pink noise algorithms, I believe.
from scipy import *
class PinkGenerator(object):
updateTable = [0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4]
updateTable.extend(updateTable[:-1])
del updateTable[-1] def __init__(self, rng=stats.norm):
self.key = 0
self.rng = rng
self.whiteValues = self.rng.rvs(size=5) def getNextValue(self):
self.key += 1
self.key = self.key % len(self.updateTable)
self.whiteValues[self.updateTable[self.key]] = self.rng.rvs()[0]
return (sum(self.whiteValues) + self.rng.rvs()[0])/6 def getManyValues(self, size):
data = zeros((size,), Float)
for i in range(size):
data[i] = self.getNextValue()
return data def sampleData(self, size=1024):
data = self.getManyValues(size)
p = power(absolute(fftshift(fft(data))), 2)/size
f = fftshift(fftfreq(size))
return data, f, p-- Robert Kern [EMAIL PROTECTED]
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