In a recent paper, a technique for designing linear phasenfrequency sampling filters was proposed that approximates a desirednfrequency response by minimizing the mean square error over thenstopbands subject to constraints on the filters amplitude response. Thisntechnique results in a large number of simultaneous linear equations thensolution of which determines the filter's impulse response. The filter'snfrequency samples which are used to implement the filter are thenndetermined by computing the discrete Fourier transform of this impulsenresponse. In this brief, a modification of this technique is developed.nThis modified technique also approximates a desired frequency responsenby minimizing the mean square error over the stopbands subject tonconstraints on the filter's amplitude response. Additionally, however,nit allows passbands to be approximated by a weighted mean square error.nThis modified technique results in a set of simultaneous linearnequations, the solution of which directly determines the filter'snnonzero frequency samples. Because the number of nonzero frequencynsamples is typically much less than the number of impulse responsenelements, this technique requires a significantly smaller number ofnsimultaneous linear equations than the other technique
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