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Multisine Approximation of Multivariate Orthogonal Random Processes

Figwer J.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 2

401-419

An approach to the synthesis and simulation of wide-sense stationary multivariate orthogonal random processes defined by their power spectral density matrices is presented. The approach is based on approximating the non-parametric power spectral density representation by the periodogram matrix of a multivariate orthogonal multisine random time-series. This periodogram matrix is used to construct the corresponding spectrum of the multivariate orthogonal multisine random time-series (synthesis). Application of the inverse finite discrete Fourier transform to this spectrum results in a multivariate orthogonal multisine random time-series with the predefined periodogram matrix (simulation). The properties of multivariate orthogonal multisine random process approximations obtained in this way are discussed. Attention is paid to asymptotic gaussianess.

Data encryption using N-lag white multisine random time-series

Niederliński A., Figwer J.

Applied Mathematics and Computer Science

1998

Vol. 8, no 3

657-670

A new data encryption method based on N-lag white multisine random time-series (WMRTS) is presented. Its essence is that consecutive characters of the cIeartext are used to generate phase shifts for all or for some of the sine components of an N-lag WMRTS. This time-series is defined in the frequency domain by its Discrete Fourier Transform (DFT). It consists of two spectra: the phase-shift spectrum containing encrypted characters and the amplitude spectrum with the same amplitude for all frequencies. This DFT is calculated with the help of the Fast Fourier Transform (FFT) algorithm transformed into the time domain. The result is the cyphertext in the form of an N-lag WMRTS. To decrypt the cyphertext, it is processed by the FFT algorithm, the result being the original DFT, from which all phase shifts are recovered. The paper presents theoretical foundations of the method and a numerical example demonstrating its effectiveness.