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