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Differential and Integrative Transformations of the Model Signals


S.A. Dudin

Differential-integral transforms (DIT) are the simplified way for signal spectrum analysis. In these transforms, the power density (variance) is calculated with using the sequentially differentiated of integrated realizations of a signal and ratio between them is evaluated. As a result, the set of data, including the power ratio between the first and the second derivatives, the ratio between the signal variance and its first derivative variance, the ratio between the double integral variance and the integral of the original signal, and so on, up to the four-time and five-time integral variance ratio. DIT coefficients for five different realizations of signals of various shapes were calculated: sinusoidal, triangular, rectangular (meander), noise signals with uniform and normal distributions, amplitude-modulated and frequency-modulated signals. Computations showed that there are essential differences between periodical and noise signals. Transformation coefficients form a horizontal line for periodic signals. Rectangular signals have other values of duty cycles in comparison with sinusoidal and triangular signals. The meander signal has maximum coefficient values. Noise signals form sloped lines of coefficients. Change of the length of realization of periodic signals yields extremums at integral ratios between the period and the length of realization, regardless of a periodic signal form. Investigations of DIT-coefficients for signals of different shapes and complexity (sinusoidal, triangular, rectangular, amplitude-modulated and frequency-modulated, noise with uniform and normal distributions) demonstrated presence of non-linear dependences of the coefficients on signals parameters. These dependences differ for sinusoidal, modulated, and noise signals that allow their detection and identification.
June 24, 2020
May 29, 2020

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