Досліджуються кусково-поліноміальні криві тре-тього степеня. Вводиться послідовність точок, які розглядаються як керуючі, а з'єднуючі їх відріз-ки є дотичними до кривої. Побудовано систему рів-нянь для обчислення коефіцієнтів кривої та знайдено умови її єдиності. На прикладах розрахунків пока-зано хороші апроксимаційні властивості одержаної кривої та проілюстрована можливість локальної зміни її форми в залежності від параметрів Ключові слова: сплайнова крива третього степе-ня, крива Без'є, параметри форми кривої Исследуются кусочно-полиномиальные кривые третьей степени. Вводится последовательность точек, рассматриваемых как управляющие, а соеди-няющие их отрезки являются касательными к кри-вой. Построена система уравнений для вычисления коэффициентов кривой и найдены условия ее един-ственности. На примерах расчетов показаны хоро-шие аппроксимационные свойства полученной кривой и проиллюстрирована возможность локального изме-нения ее формы в зависимости от параметров Ключевые слова: сплайновая кривая третьей сте-пени, кривая Безье, параметры формы кривой
This paper presents a new method for constructing a third degree parametric spline curve of C1 continuity. Like the Bèzier curve, the proposed curve is constructed and operated by control points. The peculiarity of the proposed algorithm is the assignment of some unknown values of the spline in the control points abscissas, which are based on the conditions of the first derivative continuity of the curve at these points. The position of the touch points, as well as the control points, can be set interactively. Changing of these points positions leads to a change in the curve shape. This allows the user to flexibly adjust the shape of the curve. Systems of algebraic equations with tridiagonal matrix for calculating the coefficients of a spline curve are constructed. Conditions for the existence and uniqueness of such a curve are presented. Examples of the use of the proposed curve, in particular, for monotone data sets, approximation the ellipse and constructing the letter "S" are given.
In the proposed publication, we present a geometric method for solving a boundary value problem for a nonstationary heat equation. The equivalence of the geometric solution to an explicit difference method is shown with the corresponding initial parameters. There are considered the first and second boundary value problems. The physical interpretation of the method is based on local balance.
Thus, to effectively solve the problem of eliminating the ECG baseline drift, it is necessary to filter the ECG signal. In this study for solve the problem of eliminating the ECG baseline drift, various filters were used: a low-pass filters based on the forward and inverse discrete Fourier transform, Butterworth filter, median filter, Savitsky-Golay filter. The results obtained confirmed the efficiency of filtering harmonic noise based on forward and backward DFT on real data. The method makes it possible to implement a narrow-band stop filter in the range from 0 to the Nyquist frequency. In this case, the notch band can be less than 0.1% of the Nyquist frequency, which is important when processing ECG signals.The filtering result was evaluated by the appearance of the filtered ECG. The evaluation criterion was the presence on the signal of characteristic fragments reflecting the work of the atria and ventricles of the heart in the form of a P wave, a QRS complex and a ST-T segment. A new method has been developed for filtering the ECG signal, which is based on the use of a sliding window containing 5 points. A linear function is constructed from a sample of five points using the least squares method. The value of the resulting linear function at the midpoint is used as the new value. Several iterations are performed to achieve a good result. To eliminate the baseline drift for the ECG fragment, it is proposed to use a special cubic interpolation spline. The algorithm for constructing the used spline requires solving a system of equations with a tridiagonal matrix.
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