A generalized approach to random noise synthesis: theory and computer simulation.

A generalized approach to the synthesis of Gaussian and non-Gaussian random noises as well as purely impulsive waveforms having a preselected amplitude spectrum has been developed. The basic idea behind the synthesis is to construct the amplitude-time waveform from the frequency domain, i.e., from the amplitude and phase spectra. By maintaining a predetermined (reference) amplitude spectrum and performing certain specific manipulations of the phase spectrum within any selected band of frequencies and then applying the inverse discrete Fourier transform (IDFT), peaks in the non-Gaussian random waveform can be constructed from the selected band of frequencies that have been phase manipulated. Entire families of signals can thus be produced having the same energy spectrum, but statistical characteristics that vary along the continuum from Gaussian (skewness = 0 and kurtosis = 3) through non-Gaussian (variable skewness, kurtosis, and crest factor) to purely impulsive (shock/transient) signals. The theoretical background and the results of a series of numerical simulations will be presented which demonstrate the functional relation between various phase spectrum manipulations and the descriptors of the synthesized random noise. The results show that the approach is viable and that the synthesized random waveforms can be easily tailored to simulate a variety of real-world acoustic/vibration signals, e.g., high kurtosis (impulsive) industrial noises, helicopter noises, missile vibrational signals, etc.