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This correspondence deals with the design of radar receive filters for pulse compression which optimize either the Lp-norm of the vector containing the filter sidelobe energies or the inverse signal-to-noise power ratio (ISNR) under an upper-bound constraint on the previously mentioned Lp-norm. In both the cases, we prove that the filter design can be formulated as a convex optimization second-order cone programming (SOCP) problem which can be efficiently solved with a polynomial time computational complexity resorting to interior point methods. At the analysis stage, we assess the performance of the receive filters in correspondence of different values of the parameter p highlighting the performance compromises between the integrated sidelobe level (ISL), the peak sidelobe level (PSL), and the ISNR. Finally, we study the effects of the filter length on the performance as well as the Doppler tolerance of the devised filters. The results show that the proposed technique leads to satisfactory performance levels and good Doppler tolerances.