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