It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of an FIR filter, the weighted least squares solution is equiripple. The crux of the problem in the design of equiripple filters using the weighted least squares technique lies in the determination of the necessary least squares frequency response weighting function. In this paper, a novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. From our experience, it typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response.
The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison.
In this work, estimating two-dimensional (2-D) angle of arrival for radiating sources in a coherent environment is studied. The concept of spatial smoothing is first extended to a rectangular planar array and a 2-D search function is formed t o estimate the source directions. To avoid performinga 2-0 search, an approach based on two onedimensional (1-D) searches is also discussed. This approach uses rows and columns of the rectangular array to perform I-D searches. To match the data obtained, a 2-D verification is then performed. Computer simulation results for both approaches based on the MUSIC method are presented.
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