The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special window called tight window is important because it is known to make DGT-domain processing robust to error. In this paper, we propose a method of designing tight windows that minimize the sidelobe energy. It is formulated as a constrained spectral concentration problem, and a Newton's method on an oblique manifold is derived to efficiently obtain a solution. Our numerical example showed that the proposed algorithm requires only several iterations to reach a stationary point.

翻译：短时间的 Fourier 变换( STFT) 或离散加博变换( DGT) 被广泛用于信号分析和处理。 它们的特性以窗口功能为特征。 对于信号处理来说, 设计一个称为紧凑窗口的特殊窗口很重要, 因为据知它会使 DGT- Domain 的处理发生误差。 在本文中, 我们提出了设计紧凑窗口的方法, 最大限度地减少侧边线能量 。 它被表述为受限的光谱浓度问题, 牛顿对斜体元的方法是用来有效获得解答的 。 我们的数字示例显示, 提议的算法只需要几次迭代即可到达固定点 。