Digital filter design with short transient state is a problem encountered in many fields of signal processing. In this paper a novel low-pass filter design technique with time-varying parameters is introduced in order to minimize the rise-time parameter. Through the use of calculus of variations a methodology is developed to write down the optimal closed-form expression for varying the parameters. In this concern, two cases are addressed. The ideal case in which infinite bandwidth is required and a solution of finite bandwidth. The latest is obtained by means of a proper restriction in the frequency domain. The proposed filter achieves the shortest rise-time and allows better preservation of the edge shape in comparison with other reported filtering methods. The performance of the proposed system is illustrated with the aid of simulations.
The recent discovery of the Ledenyov digital waves in the economies of scale and scope led to an origination of considerable scientific interest in the modeling of new types of the discrete-time digital signals generators for the business cycles generation in the macroeconomics. Article aims: 1) to model the discrete-time digital signals generators for the business cycles generation in the macroeconomics, 2) to demonstrate the technical differences between the new model of the discrete-time digital signals generator and the existing models of the continuous-time (continuous wave) signals generators in the macroeconomics; 3) to accurately analyze the spectrum of discrete-time digital signals in the economies of scale and scope, 4) to improve the Ledenyov discrete time digital signals theory to precisely characterize the discrete time digital signals in the macroeconomics, 5) to better develop the complex software program to forecast the business cycles, going from the spectral analysis of the discrete time digital signals and the continuous time signals in the nonlinear dynamic economic system over the selected time period. The developed MicroSA software program intends: 1) to perform the spectrum analysis of the discrete-time digital signals and the continuous-time signals in the macroeconomics; 2) to make the computer modeling and to forecast the business cycles, going from the spectral analysis of the discrete time signals and the continuous time signals in the macroeconomics. The MicroSA can be used by a) the central banks with the purpose to make the strategic decisions on the monetary policies, financial stability policies, and b) the commercial/investment banks with the aim to make the business decisions on the minimum capital allocation, countercyclical capital buffer creation, and capital investments. 2b1af7f3a8