The design of compensation filters for comb decimators using amplitude transformation is introduced. It is shown that the transformation of cosine-squared filters provides good compensation characteristics. For a first-degree polynomial, the slope of the transformation line is explicitly set as the unique compensator's multiplierless coefficient. This coefficient changes proportionally with the increase of the comb passband droop. Thus, the proposed approach provides an intuitive and easy way of designing compensation filters.
We have developed several methods of designing sparse periodic arrays based upon the polynomial factorization method. In these methods, transmit and receive aperture polynomials are selected such that their product results in a polynomial representing the desired combined transmit/receive (T/R) effective aperture function. A desired combined T/R effective aperture is simply an aperture with an appropriate width exhibiting a spectrum that corresponds to the desired two-way radiation pattern. At least one of the two aperture functions that constitute the combined T/R effective aperture function will be a sparse polynomial. A measure of sparsity of the designed array is defined in terms of the element reduction factor. We show that elements of a linear array can be reduced with varying degrees of beam mainlobe width to sidelobe reduction properties.
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