# frequency symbolic method

## Application of the frequency symbolic method for the analysis of a quadrature demodulator of a telecommunication system

The paper presents the analysis of the operation of a quadrature demodulator of a signals modulated with the use of Quadrature Phase Shift Keying (QPSK) taking into account the influence of parameters of a low-pass filter. Such quadrature demodulators are used in modern telecommunication systems because of the problem of separating out two Phase Shift Keying (PSK) modulated signals (in-phase and quadrature) from the QPSK-modulated signal arising at the receiving end, which is followed by detecting and determining the binary signal as “one” or “zero”.

## Optimization of parametric balanced modulator based on frequency symbolic method

Application of the frequency symbolic method for analysis of established modes of linear periodically time-variable (LPTV) circuits to solving an optimization task conditioned by the control of their asymptotic stability is considered. The results of optimization of a parametric balanced modulator with respect to the criterion which is based on calculation of the parametric transfer functions approximated by Fourier trigonometric polynomials are presented.

## Tolerance analysis and optimization of linear periodically time-variable circuits based on the frequency symbolic method

The paper presents the procedures of tolerance analysis and optimization of linear periodically time-variable circuits, based on the frequency symbolic method and realized by the system of functions MAOPCs in an environment MATLAB.

## Application of the frequency symbolic method for analysis of linear periodically-time-variable circuits in the time domain

This paper focuses on the problem of using the symbolic frequency method for the determining the time dependency of output signals of linear periodically-time-variable circuits by applying the inverse Fourier transform (for a steady-state mode) or the Laplace transform (for a transition mode) to the images of these signals obtained using the transfer functions.

## The system maopcs for the multivariate analysis and optimization of linear parametric circuits at the enviroment of matlab

This paper considers the software realization the system of functions MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits) for multivariate analysis and optimization of linear parametric circuits based on frequency symbolic method. This method is based on the formation of the approximated transfer functions of linear parametric circuits in the form of Fourier trigonometric polynomials.

## Specifics of determination sensitivity of linear parametric circuits in the frequency domain

In software which are dedicated for the design of electronic circuits with constant parameters is widely used function of sensitivity, which allows you to focused  solve the tasks of multivariate  analysis and optimization of such circuits. The function of sensitivity of linear parametric circuits not used widely because there was no reliable methods of symbolic computation of parametric transfer functions.

## About the decrease bulkiness of mathematical model of linear periodically time-variable circuit

In this paper are investigated the influence of variables the differential equation describing the linear periodically time-variable circuits in the time domain on decrease of bulkiness such equation. Rules of forming a system of linear differential equations of circuit that provide its acceptable bulkiness are proposed. Communication of voltages and currents on elements of an electric circuit looks like algebraic, differential and integral equations.

## Investigation of Stability of Parametric Amplifiers in an Environment MAOPCs

The paper considers the question of the research of assessment of the stability of linear periodically time-variable circuits by the frequency symbolic method. The function system MAOPCs, which is based on the frequency symbolic method, is an effective tool of investigation of linear periodically time-variable circuits and in particular parametric amplifiers.

## The Expansion of the Possibilities of the System Program Functions MAOPCS for the Study of Linear Periodically-time-variable Circuits

The system program function MAOPCs is designed to study multivariate analysis and optimization of state linear periodically-time-variable circuits.

The architecture of the system MAOPCs is based on the principles of softwareMatlab environment, which provides the existence of the independent the software functions and creating the user-defined functions, and because it is an open system, it allows you to supplement it with the new functions.