If it should not be "realistic" you could use a sum of sines approach.

E.g.

nSines = 100;

SampleRate = 1000;

fMin = 0;

fMax = 100;

t = linspace(0,1,SampleRate);

As = rand(nSines,1);

Fs = linspace(fMin,fMax,nSines)';

Y = sum(As*ones(size(t)).*sin(2*pi*Fs*t));

plot(Y);

Replace ones(size(t)) with a time-variant scaling function for the amplitudes.

Repace rand(nSines,1) with a vector of chosen amplitudes for the given frequencies.

It's simplistic but it gives you quasi-random EEG-like signal...

You could use something like a Jansen-Rit model (which can produce alpha-like oscillations and evoked potentials) or generate white gaussian noise, transform it to the frequency spectrum, multiply it with a realistic PSD (possibly obtained from real EEG data), and then transform back to the time domain.

You can also use the Matlab Commande : ecg(). Bellow an example given in Matlab :

EXAMPLE:

x = ecg(500).';

y = sgolayfilt(x,0,3); % Typical values are: d=0 and F=3,5,9, etc.

y5 = sgolayfilt(x,0,5);

y15 = sgolayfilt(x,0,15);

plot(1:length(x),[x y y5 y15]);

Thank you very much for answers. As I try to find the best matching solution for this problem I came to the following:

Quasi-random signal can be generated by summing i partial signals multiplied by their individual weight, and adding to that a radnom noise value. All of this can be expressed by:

"Equation 1.jpg" 

...where wi is signals' individual weight, f(t)i is a signal, and rani is our random noise value, which changes with each i iteration. Finally, i is the total number of "merged" signals.

We can now look on simple example with three signals:

"Equation 2.jpg" and "Equation 3.jpg"

The drill shown in the "Equation 3.jpg" has to be of course applied to all t values from a given range.

Hello,

Thanks for your nice question still opened for new vistas.

I have published with JC Levy two articles related to your question in 1972 and 1973 which can give you new ideas  :

1) J.C. LEVY, P. ETEVENON

Un modèle d'électroencéphalogramme artificiel comparé aux tracés veille-sommeil du rat. Symposium "Vigilance, sommeil et rêve", 4, 695-701, dans Psychologie médicale, Paris, 1972

2) P. ETEVENON, J.C. LEVY

Simulation sur ordinateur d'électroencéphalogrammes normaux pathologiques. Journées d'Informatique Méd., 265-281 dans "Colloque de l'IRIA", Domaine de Vauluçau, 78, Rocquencourt, 1973

I will download the files of these two articles below which are based on non-linear models of EEG, 3) Other non-linear models have also been published by Fernando Lopes da Silva.

4) You may also found answers from my D.Sc. thesis of 1977 that I have already fully downloaded in my ResearhGate Publications and where at the end you may find the first application of Hilbert transform to EEG instead of FFT and considered into a broader model of EEG as an electrophysiological type of radiocommunication, 

5) This is why John Barlow quoted me later in his very important book on EEG :

John S. Barlow

The ELECTROENCEPHALOGRAM. Its Patterns and Origins.

A Bradford Book, The MIT Press, Cambridge, Massachussets, and London, England, ISBN 780262023542 90000

You may also look at the books and articles of PL Nunez and RB Silberstein like  : 

6) A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging.

Nunez PL, Silberstein RB, Cadusch PJ, Wijesinghe RS, Westdorp AF, Srinivasan R., Electroencephalogr Clin Neurophysiol. 1994 Jan;90(1):40-57

7) Spatial filtering and neocortical dynamics: estimates of EEG coherence.

Srinivasan R, Nunez PL, Silberstein RB.

IEEE Trans Biomed Eng. 1998 Jul;45(7):814-26.

i hope this can be useful for your research.

Best regards and the best for you in 2015.

Pierre Etevenon, DSc,PhD

Directeur de Recherche honoraire INSERM

Additional to the great material offered in the other answers, I think this is the perfect complement of what I think you are looking for: https://github.com/pchrapka/phasereset

Hi,

please see the following paper to know about simulated EEG signal generation:

Article Modified Dominant Mode Rejection Beamformer for Localizing B...

for example

y = ecg(1024);