I.I. Orlov, A.V. Oinats

The known mathematical model of the narrowband signal is representation it in the form of the linear combination of quadrature signals which represent informational part of the signal. In the paper we present a common description of the signal propagation through linear systems that is convenient for quadrature signals. We introduced a two-dimensional vector with components that are real and imaginary parts of the signal function. The initial signal and any linear operations can be presented using two-dimensional matrices in the context of the suggested scheme. Particularly we introduced vector-valued Duamel integral and matrix transfer function of the linear system. Among description of the common properties of the linear systems suggested method is applied for narrowband signal propagation through linear time-dependent system with specified properties. We obtained an expression for output signal of the linear time-dependent system that is similar to corresponding expression in the linear stationary system. The difference is that weakening, time delay and phase taper are dependent on time. Obtained formulas evidently point at the signal shape distortion caused by dispersion of the transfer function absolute value. We discussed the application of the obtained formulas to analysis of the narrowband signal propagating through time-dependent channel of the vertical and oblique sounding of the ionosphere. We noted that consideration of the multi-channel (multiradiate) physical systems and propagation of the wideband signals can be reduced to presented scheme.