A method and device for the generation of a random signal, comprising: A first step (a) for the generation of a pseudo-random signal, a second step (b) for the filtering (F1) of the signal coming from the step (a) to obtain a signal x(t) having a predetermined spectral envelope H(f), a third step (c) in which a non-linear function g is applied to the signal x(t) so as to form a signal y(t) and create overshoots on the edges of the histogram of the signal y(t), a fourth filtering (F2) step (d) used to smoothen the overshoots of the histogram of the signal y(t), compensate for the effect of the non-linearity and carry out an additional filtering at (F1). Application to a system of analog-digital conversion or digital-analog conversion.