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- W1510098889 abstract "Under certain conditions, a frequency sampling filter can implement a linear phase filter more efficiently than an equivalent filter implemented by a direct convolution structure. However, the system function of a frequency sampling filter requires pole-zero cancellations on the unit circle. For practical implementations, finite word length effects usually prevent exact pole-zero cancellation which can result in filter instability. To prevent instability, the poles and zeros on the unit circle can be moved to a circle of radius r where 0 < r < 1 by replacing z- 1 with rz− 1 in the filter’s system function. The resulting filter is guaranteed to be stable; however, the filter’s magnitude and phase characteristics are affected by the choice of r. This chapter develops a method for determining optimal coefficients which minimizes a linear combination of the mean square error in the stopband and passband, and the sum of square error of the impulse response symmetry subject to passband and stopband constraints and a fixed value of r < 1. The optimization problem is solved using the Lagrange multiplier optimization method which results in a set of linear equations, the solution of which determines the filter’s coefficients." @default.
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- W1510098889 date "1995-01-01" @default.
- W1510098889 modified "2023-09-27" @default.
- W1510098889 title "The Design of Frequency Sampling Filters" @default.
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- W1510098889 doi "https://doi.org/10.1016/s0090-5267(06)80040-x" @default.
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