On linear time-varying system characterizations

Time-frequency responses of generalized first order parametric sections

“…Parametric system frequency responses are defined in two ways [4,8]. The first of them is identical to the one concerning stationary systems and consists in defining the frequency characteristics as the ratio of the complex output signal to the complex monoharmonic input signal.…”

“…It consist in the application of the double Fourier transform with respect to the impulse function h(t, τ). It is called a bispectral frequency response [4]. The mentioned method of describing LTV system frequency properties is not used in this paper.…”

Modelling of the First-Order Time-Varying Filters with Periodically Variable Coefficients

“…In the domain oftransform or -transform, algebra is based on the classical definition of the algebraic sum and the multiplication operations (±, ⋅) with arguments being the transfer functions or spectral functions of elementary blocks. In the case of LTV systems with coefficients variable in time, the classical definition of operational transfer functions has no sense [1,35].…”

“…The transfer function and the frequency response for LTV systems can be defined in various ways [1,12,[36][37][38]. The most popular definitions have been given below:…”

“…Those systems are a direct generalization of classical linear and time invariant (LTI) systems. Many theoretical works [1][2][3][4][5] as well as practical applications have been devoted to these systems. In particular, LTV systems can be applied in signal processing [6][7][8][9][10][11], especially in sampling systems [12], signal filtering and noise reduction [7,8,[13][14][15][16][17], and current compensators in power networks [18,19], amplifiers [5,20], chaos generators [21], electromagnetic launchers [22], and medical devices [23].…”