A new closed form method for design of variable bandwidth linear phase FIR filter using different polynomials |
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| Affiliation: | 1. PDPM Indian Institute of Information Technology Design and Manufacturing, Jabalpur 482005, MP, India;2. Indian Institute of Technology Patna, Patna 800013, Bihar, India;3. Department of Electrical Engineering, Indian Institute of Technology Roorkee, Uttrakhand 247667, India;1. Departamento de Ciencias Farmacéuticas, Facultad de Ciencias, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile;2. Departamento de Física, Facultad de Ciencias, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile;3. Departamento de Química, Facultad de Ciencias Básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile;4. Instituto de Física, Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile;5. Center for the Development of Nanoscience and Nanotechnology, CEDENNA, Santiago, Chile;1. Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan;2. WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan;1. Department of ECE, National Institute of Technology Calicut, Calicut, Kerala, India;2. Qualcomm India Pvt. Ltd., Bangalore, India;1. Universidad Autónoma del Estado de México, UAEM, Centro Conjunto de Investigación en Química Sustentable CCIQS, UAEM-UNAM, Carretera Toluca-Atlacomulco, km 14.5, C.P. 50200 Toluca, Estado de México, Mexico;2. Department of Chemistry, Xavier University of Louisiana, 1 Drexel Drive, New Orleans, LA 70125, United States |
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| Abstract: | 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 polynomials and shifted Legendre polynomials is proposed. For this purpose, the transfer function of a variable bandwidth filter, which is a linear combination of fixed-coefficient linear-phase filters and the above polynomials are separately exploited as tuning parameters to control bandwidth of the filter. In order to determine the filter coefficients, mean squared difference between the desired variable bandwidth filter and the practical filter is minimized by differentiating it with respect to its coefficients leading to a system of linear equations. The matrix elements can be expressed in form of Toeplitz-plus-Hankel matrix, which reduces the computational complexity. Several examples are included to demonstrate effectiveness of the proposed method in terms of passband error (ep), stopband error (es) and stopband attenuation (As). |
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| Keywords: | Variable bandwidth filter Chebyshev, Bernstein, and Legendre polynomials FIR |
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