Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics | EURASIP Journal on Applied Signal Processing 2004 13 2053-2065 2004 Hindawi Publishing Corporation Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics Stuart W. A. Bergen Department of Electrical and Computer Engineering University of Victoria P. O. Box 3055 STN CSC Victoria BC Canada VSW 3P6 Email sbergen@ Andreas Antoniou Department of Electrical and Computer Engineering University of Victoria P. O. Box 3055 STN CSC Victoria BC Canada VSW 3P6 Email aantoniou@ Received 7 April 2003 Revised 17 January 2004 Recommended for Publication by Hideaki Sakai A method for the design of ultraspherical window functions that achieves prescribed spectral characteristics is proposed. The method comprises a collection of techniques that can be used to determine the three independent parameters of the ultraspherical window such that a specified ripple ratio and main-lobe width or null-to-null width along with a user-defined side-lobe pattern can be achieved. Other known two-parameter windows can achieve a specified ripple ratio and main-lobe width however their side-lobe pattern cannot be controlled as in the proposed method. A comparison with other windows has shown that a difference in performance exists between the ultraspherical and Kaiser windows which depends critically on the required specifications. The paper also highlights some applications of the proposed method in the areas of digital beamforming and image processing. Keywords and phrases window functions ultraspherical window beamforming image processing digital filters. 1. INTRODUCTION Windows are time-domain weighting functions that are used to reduce Gibbs oscillations resulting from the truncation of a Fourier series. Their roots date back over one-hundred years to Fejer s averaging technique for a truncated Fourier series and they are employed in a variety of traditional signal processing applications including power spectral estimation beamforming and digital .
