Abstract—In Digital Signal Processing, one of the most important filter type is the FIR filter which can be designed via various methods. Window technique is the most important technique that is used to design the FIR filter. Apart from various window techniques, Dolph-Chebyshev window has the subject of importance for the design of the FIR filter in efficient way. In this paper, the design met...

In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

In this paper we propose the use of a technique based on Chebyshev polynomials approximation for determining the minimum-time rest-to-rest openloop control law for multi-input multi-output (MIMO) continuous-time systems with input and output constraints. The optimal input can be determined, without discretising the system, by suitably approximating the state variables and the input signals by m...

The field of values and pseudospectra are useful tools for understanding the behaviour of various matrix processes . To compute these subsets of the complex plane it is necessary to estimate one or two eigenvalues of a large number of parametrized Hermitian matrices; these computations are prohibitively expensive for large, possibly sparse, matrices, if done by use of the QR algorithm . We desc...

The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the ...

We present an approach for the acceleration of the restarted Arnoldi iteration for the computation of a number of eigenvalues of the standard eigenproblem Ax = x. This study applies the Chebyshev polynomial to the restarted Arnoldi iteration and proves that it computes necessary eigenvalues with far less complexity than the QR method. We also discuss the dependence of the convergence rate of th...

From a dynamical point of view applied to complex polynomials, we study a number of root–finding iterative methods. We consider Newton’s method, Newton’s method for multiple roots, Jarratt’s method, the super–Halley method, the convex as well as the double convex acceleration of Whittaker’s method, the methods of Chebyshev, Stirling, and Steffensen, among others. Since all of the iterative root...

The paper presents an application of digital filtering in data processing of acceleration records from earthquakes. Butterworth, Chebyshev, and Bessel filters with different orders are considered to eliminate the frequency noise. A dataset under investigation includes accelerograms from three stations, located in Turkey (Dinar, Izmit, Kusadasi), all working with an analogue type of seismograph ...

The paper presents an application of digital filtering in data processing of acceleration records from earthquakes. Butterworth, Chebyshev, and Bessel filters with different orders are considered to eliminate the frequency noise. A dataset under investigation includes accelerograms from three stations, located in Turkey (Dinar, Izmit, Kusadasi), all working with an analogue type of seismograph ...