A Computationally efficient technique for designing frequency sampling filters
In a recent paper, a technique for designing linear phase frequency sampling ﬁlters was proposed that approximates a desired frequency response by minimizing the mean square error over the stopbands subject to constraints on the ﬁlters amplitude response. This technique results in a large number of simultaneous linear equations, the solution of which determines the ﬁlter’s impulse response. The ﬁlter’s frequency samples which are used to implement the ﬁlter are then determined by computing the discrete Fourier transform of this impulse response. In this brief, a modiﬁcation of this technique is developed. This modiﬁed technique also approximates a desired frequency response by minimizing the mean square error over the stopbands subject to constraints on the ﬁlter’s amplitude response. Additionally, however, it allows passbands to be approximated by a weighted mean square error. This modiﬁed technique results in a set of simultaneous linear equations, the solution of which directly determines the ﬁlter’s nonzero frequency samples. Because the number of nonzero frequency samples is typically much less than the number of impulse response elements, this technique requires a signiﬁcantly smaller number of simultaneous linear equations than the other technique.
Digital filters (Mathematics); Electric filters; Finite impulse response (FIR); Frequency sampling ﬁlter; Linear phase; Narrowband ﬁlters
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A Computationally efficient technique for designing frequency sampling filters.
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 44(1),