Efficient Design of Scaled Rectangular (Saramäki) Window

A rectangular-window sidelobe magnitude reduction method by widening the main lobe width was proposed in [1]. In [2], a technique for trading off main lobe width against sidelobe magnitude for any arbitrary window was reported; a fast convergence algorithm for its implementation was proposed in [3]. In [3], the derivatives of the window function are expressed in Chebyshev polynomials which have high arithmetic complexity. All the coefficients of a rectangular-window are equal; this special property is exploited, in this paper, for deriving the window functions derivatives without the use of Chebyshev polynomials resulting in a great reduction in the arithmetic complexity.