请教：已知功率谱密度函数，如何反求时间序列？

Labview中有一些vi，可以产生指定分布的随机信号。现在需要产生一个满足高斯分布，功率谱密度函数为 PSD()=a/(b+f^2)的随机序列，如何实现？
如果从PSD定义入手，反傅立叶变换得到自相关函数，如何进一步求得时间函数？

Since the Fourier transform is complex, you need both real+imaginary,  or magnitude+phase, to reconstruct the time signal. PSD only contains the magnitude info, so you can obtain the time signal if you also have the phase info.

偶不需要唯一确定，只要得到满足高斯分布方差，以及PSD()函数的随机序列。
偶可否任意假设一组相位信号？
在已知幅值、相位信息的条件下，具体如何计算？

If you look at the properties of the Fourier transform, you will see that different phase information will lead to different time trace.
Once you have both mag and phase, you can combine them as a complex sequence and directly use the inverse FFT to obtain the time signal.