计算泰勒窗。泰勒加权函数

The Taylor window is a type of window function that is commonly used in digital signal processing to reduce spectral leakage when analyzing a signal. It is defined as:

w(n) = [1 - (n/N)^2] / [1 + (n/N)^2]

where n is the index of the current sample, N is the total number of samples in the window, and ^2 denotes squaring.

The Taylor weighting function is a generalization of the Hamming window that is designed to provide better control over the trade-off between spectral leakage and time-domain sidelobe levels. It is defined as:

w(n) = 1 - a[1 - cos(2πn/N)] + a^2[1 - cos(4πn/N)] - a^3[1 - cos(6πn/N)] + ...

where a is a parameter that controls the shape of the window. When a is set to zero, the Taylor window reduces to the rectangular window; as a increases, the sidelobe levels decrease at the expense of increased spectral leakage.