## 2 About the Frequency Symbolic Method  
The frequency symbolic method (FSM) is based on the following fundamental concepts [15]:  
1. Consider the LPTV circuit where: * There are one or more parametric elements, whose parameters change periodically over time with the same period \(T\) (in the simplest version),There is one input with an input signal \(x(t)\) and one output with a response \(y(t)\). 2. Such an LPTV circuit in the time domain can be described by the symbolic system of linear differential equations (SSLDE). 3. By eliminating internal variables in the SSLDR using one of the known methods, one can obtain a differential Equation (1) describing the circuit. \[a_{n}(t)y^{(n)}+a_{n-1}(t)y^{(n-1)}+\ldots+a_{0}(t)y=b_{m}(t)x^{(m)}+b_{m-1}(t)x ^{(m-1)}+\ldots+b_{0}(t)x,\] (5) where \(y(t)\) is the output (sought) and \(x(t)\) is the input (set) variable, \(t\) is the independent variable (time), and \(a_{i}(t)\), \(b_{j}(t)\) are parametric functions of time \(t\). 4. For an LPTV circuit described by the differential Equation (5), using the equation of [PERSON] [1], we determine the differential equation describing this circuit in the frequency domain: \[\frac{1}{n!}\frac{d^{n}A(s,t)}{ds^{n}}\frac{d^{n}W(s,t)}{dt^{n}}+...+\frac{dA( s,t)}{ds}\frac{dW(s,t)}{dt}+A(s,t)W(s,t)=B(s,t),\] (6) where: \[W(s,t)=\frac{Y(s,t)}{X(s,t)},\] (7) is the transfer function of the LPTV circuit, and: \[A(s,t)=a_{n}(t)s^{n}+...+a_{1}(t)s+a_{0}(t),\] (8) \[B(s,t)=b_{m}(t)s^{m}+...+b_{1}(t)s+b_{0}(t),\] (9) are the corresponding time-dependent periodic functions of time \(t\) with period \(T\) coefficients of Equation (1), whereas \(Y(s,t)\) and \(X(s,t)\) are the images of the output and input variables in the frequency domain, respectively, and \(s\) is a complex variable. 5. In general, Equation (6) does not have an exact analytical solution, so one must find an approximate solution that accounts for both the known properties of the desired transfer function \(W(s,t)\) and the specifics of the algorithm used for its determination: (a) The approximation \(\hat{W}(s,t)\) of the transfer function \(W(s,t)\) must achieve a predefined accuracy level of choice, (b) Given that \(\hat{W}(s,t)\) needs to undergo \(n\)-times differentiation when inserted into (6), it should be represented by a function that allows straightforward differentiation (i.e., intricate fractions, etc.). Consequently, for solving (6), one can suggest an approximation of the transfer function by a trigonometric Fourier series: \[W(s,t)=W_{0}(s)+\sum_{i=1}^{k}\left[W_{ci}(s)\text{cos}(\Omega t)+W_{si}(s) \text{sin}(\Omega t)\right],\ \Omega=\frac{2\pi}{T},\] (10) or in a complex form: \[\hat{W}(s,t)=W_{0}(s)+\sum_{i=1}^{k}[W_{-i}(s)\text{exp}(i\Omega t)+W_{+i}(s) \text{exp}(i\Omega t)].\] (11)  
The frequency symbolic method of solution to (6) finding is as follows:  
Step 1. One of the expressions (11) or (13), for instance, Equation (11) is differentiated \(n\) times with respect to the variable \(t\). The resulting derivatives, along with the original expression, are then substituted into (6). Step 2. By transferring the right-hand side of expression (6) to the left side, one can obtain the following algebraic expression:  
\[\delta(W_{0},W_{c1},W_{s1},W_{c2},W_{s2},...,W_{ck},W_{sk})=0. \tag{12}\]The functional \(\delta(\cdot)\) described by (13) is periodic with period \(T\) and contains \((2k+1)\) unknowns \(W_{0}\), \(W_{c1}\), \(W_{51}\), \(W_{c2}\), \(W_{52}\),..., \(W_{ck}\), \(W_{sk}\), which need to be determined. Step 3. As the functional \(\delta(\cdot)\) is periodic, we decompose it into a Fourier series with period \(T\). According to (13), we equate \(k\) harmonics and the constant component of this series to zero. This results in a system of \((2k+1)\) linear algebraic equations, which form a symbolic system of linear algebraic equations (SSLAE) of the \((2k+1)\) order with \((2k+1)\) unknowns. Step 4. The solution of the resulting SSLAE determines the desired unknowns of expression (8) and approximates (11) or (12).