THE PROBABILITY-DENSITY FUNCTION OF A FOURIER LINE

It is usually assumed that the probability-density function of a line in a power spectrum is given by the product of chi(2)2. This assumptio n rests on the hypothesis that Fourier points are statistically indepe ndent which is true only in the limit of an infinite observation time without any interruption in the data. We give a more accurate expressi on of that probability-density function and a rigorous one for the rea lization of a Fourier spectrum which can also be used to obtain the li ne parameters with the maximum likelihood method. One other interest o f these formulae is that they provide an accurate method for line deco nvolution. The theory is given both for uninterrupted and for interrup ted sequences of data. Also we extend to this latter case results obta ined earlier.