| Random numbers with predefined spectral density [message #4853] |
Mon, 21 August 1995 00:00  |
hahn
Messages: 108
Registered: November 1993
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Senior Member |
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Hi,
I want to calculate random numbers with other than white noise
spectrum. The noise spectrum (amplitude vs. frequency) is
given and I need random numbers that adhere to this spectrum.
Actually, the spectrum is given by a FIR filter of order 12:
coeff = [ 1.48, 1.64, 0.927, ..., 3.1e-3]
How to proceed from here ?
Norbert Hahn
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| Re: Random numbers with predefined spectral density [message #4926 is a reply to message #4853] |
Thu, 24 August 1995 00:00  |
David Ritscher
Messages: 30
Registered: August 1995
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Member |
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> I want to calculate random numbers with other than white noise
> spectrum. The noise spectrum (amplitude vs. frequency) is
> given and I need random numbers that adhere to this spectrum.
> Actually, the spectrum is given by a FIR filter of order 12:
> coeff = [ 1.48, 1.64, 0.927, ..., 3.1e-3]
Just make a white noise sequence and filter it, using these same
coefficients, as per the following example:
coeff = [ 1.48, 1.64, 0.927, 0, 0, 3.1e-3]
n_samples = 10000
n_coef = n_elements(coeff)
n_samples = 10000 + 2*n_coef
white = randomn(seed, n_samples)
colored = convol(white, coeff) ;filter the white noise source
; throw away the first and last values, some of which were not filtered:
colored = colored(n_coef:n_samples-1-n_coef)
; note - although the IDL/PVWave CONVOL funtction is not really a
; convolution (i.e., (convol(a, reverse(b)) really performs the convolution
; of a and b), since this order doesn't change the spectrum of the result,
; this consideration can be ignored.
--
David Ritscher
Raum 47.2.279
Zentralinstitut fuer Biomedizinische Technik (ZIBMT)
Universitaet Ulm
D-89069 ULM
Germany
Tel: ++49 (731) 502 5313
Fax: ++49 (731) 502 5343
or 5317
internet: david.ritscher@zibmt.uni-ulm.de
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| Re: Random numbers with predefined spectral density [message #4945 is a reply to message #4853] |
Tue, 22 August 1995 00:00 |
steinhh
Messages: 260
Registered: June 1994
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Senior Member |
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In article <41ab22$jp5@rs18.hrz.th-darmstadt.de>, hahn@hrz.th-darmstadt.de (Norbert Hahn) writes:
|>
|> I want to calculate random numbers with other than white noise
|> spectrum. The noise spectrum (amplitude vs. frequency) is
|> given and I need random numbers that adhere to this spectrum.
|>
|> Actually, the spectrum is given by a FIR filter of order 12:
|> coeff = [ 1.48, 1.64, 0.927, ..., 3.1e-3]
|>
|> How to proceed from here ?
|>
|> Norbert Hahn
Simply produce white noise, and filter it with your desired noise
spectrum (beware of the difference between *amplitude* and the
*power* spectrum).
Given N = Noise amplitude vs. frequency, an array with NN elements,
you simply use:
NOISE = fft( fft(randomn(seed,NN),-1)*N , 1)
You should also include some renormalization of the total power
in your noise, of course.
Stein Vidar
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