Nischal Piratla wrote: > Hi all, > I would like to rephrase my question to clear the confusion. > If the convolution of f(t) and f(-t) is a Gaussian, then is there > anything that we can say about f(t)! For one I can see that f(t) > itself could be a Gaussian. Can it be any other known distribution?
See for example "Characteristic Functions" by E Lukacs, Griffin, London 1969, ... on page 243 (section 8.2) Theorem 8.2.1 (Cramer's Theorem) ... The characteristic function of the normal distribution has only normal factors. (normal == Gaussian here) (Here multiplication of characteristic functions is equivalent to convolution of distributions ... you will need to be careful of how this applies to your original question relating to correlations and (?) decomposition of correlations/spectra into impulse response functions) There may well be other slightly different routes to similar characterisations of the Normal distribution ... I would start by looking in the well-known books by Johnson & Kotz on families of distributions. David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
