A technique for trading off the main lobe width against sidelobe magnitude for any arbitrary window was reported in Lim et al. and subsequently, a fast convergence method for its implementation was proposed by the same authors. These methods require the computation of derivatives involving the evaluation of trigonometric and hyperbolic functions. In this paper, we show that the derivatives can be computed without evaluating trigonometric and hyperbolic functions if the window function is a sum of exponentials such as a Fourier series.

中文翻译：

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以指数和表示的窗函数的有效缩放

Lim 等人报道了一种在任意窗口中权衡主瓣宽度与旁瓣幅度的技术。随后，同一作者提出了一种快速收敛的实现方法。这些方法需要计算涉及三角函数和双曲函数评估的导数。在本文中，我们展示了如果窗函数是诸如傅里叶级数之类的指数之和，则无需评估三角函数和双曲函数即可计算导数。