Computational Efficiency of Interpolated Band-Stop Filters for Even Spectral Bands

Band-stop filters are discussed. Based on the previously proposed structure for odd spectral bands, a block diagram of an interpolated band-stop filter for even spectral bands was created. Using the proposed structure will reduce the requirements for computing resources, namely the number of filter coefficients in comparison with the reference filter calculated by the classical method. For this structure, relations were obtained to determine its computational efficiency, as well as the register increase coefficient. The following parameters are analytically determined: the optimal meaning of the interpolation coefficient, the maximum meaning of the computational efficiency and the register increase coefficient at the optimal meaning of the interpolation coefficient. A feature of the obtained relations is that they use the values of the stopband and the central frequency of the rejection in determining the parameters necessary for the synthesis of the interpolated FIR filter. A comparison was made of the interpolated band-stop filter for even spectral bands according to the proposed structure and the reference band-stop filter synthesized by the classical method. The performed analysis showed that it is expedient to use the proposed structure under certain conditions. The disadvantages of the recommended structure include the fractionality of the resulting interpolation coefficient, the discreteness of switching between spectral bands and the increase in ripples in the resulting frequency response. We can assume that the proposed structure is effective but not universal.