The short-time Fourier transform has been shown to be a powerful tool for non-stationary signals and time-varying systems. This paper investigates the signal moments in the Hardy-Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non-smooth signals if we replace the classical derivatives by the Hardy-Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short-time Fourier domain are established in the Hardy-Sobolev space.