Multisine transformation - Properties and applications

Multisine time-series are sums of discrete-time sines with deterministic amplitudes and phase shifts chosen in a special way. In this paper a new recursive approach to synthesis and simulation of multisine time-series with predefined spectral properties, is presented. On the basis of the power spectral density function and phase shifts chosen with some well-defined properties, the finite discrete Fourier transform of multisine time-series is synthesised and the corresponding multisine time-series is simulated by performing an inverse discrete Fourier transform of the synthesised spectrum. In the approach the phase shifts needed to synthesise and simulate N -sample multisine random time-series are calculated using N/2-sample multisine time-series obtained in the previous iteration. A transformation of the phase shifts into the corresponding N-sample multisine time-series is called a multisine transformation. Its properties are discussed. Applications of the multisine transformation to generation of uniformly distributed random numbers as well as to simulation of realisations for multisine approximations of wide-sense stationary random processes given by their power spectral densities are included.