This paper presents a set of windows, called sum-cosine windows, whose first side-lobe level varies from −39-30 to − 67-66dB, while the peak sidelobe offers −39-30 to − 6312dB attenuation. The asymptotic decay rate of the sidelobe envelope ranges from 12dB per octave to 36dB per octave. However, the main-lobe width of these windows falls in between Hamming and Blackman windows and Black-man windows and the optimum windows, proposed by Harris and Nuttall. The distinct advantage of these windows is their simple form, resulting in easy implementation, compared to the near-optimum windows proposed by Kaiser. © 1985 Taylor & Francis Group, LLC.