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The output signal of the LFM pulse compression filter is analyzed in order to look into causes of discrepancy between the sidelobe level obtainable using standard taper windows with the literature-reported data. The case of applying window functions in the form of cosine harmonics of the Fourier series, which describes a rather great number of the standard windows, is analyzed in detail. Analytical expressions are presented for the output signal of the chirp-pulse compression filter with such windows and for the amount of loss in the signalto-noise ratio (SNR). Coefficients of window functions containing 2 cosine harmonics of the Fourier series have empirically been selected that made it possible to improve sidelobe suppression by approximately 0.34 dB for B = 21 and more than by 1 dB for B = 7 as compared with the Hamming window. The obtained results allow concluding that the optimization problem for the window function parameters in the case of small pulse duration-bandwidth products should be solved individually for each specific value of B. Keywords ? LFM pulse, pulse compression filter, window function, sidelobe level