A new closed form method for design of variable bandwidth linearphase FIR filter using different polynomials - Kumar, A.; Suman, S.; Singh, G.K. (Elsevier, 2014)
In this paper, a new method for the design of variable bandwidth linear-phase finite impulse response(FIR) filters using different polynomials such as shifted Chebyshev polynomials, Bernstein polynomi-als and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variablebandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the abovepolynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order todetermine the filter coefficients, mean squared difference between the desired variable bandwidth filterand the practical filter is minimized by differentiating it with respect to its coefficients leading to a systemof linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, whichreduces the computational complexity. Several examples are included to demonstrate effectiveness ofthe proposed method in terms of passband error (ep), stopband error (es) and stopband attenuation (As).