This paper examines the effects of random jitters in sampling locations upon power spectrum estimation. Random jitters in sampling locations introduce phase shifts in corresponding Fourier coefficients and lead to, among other distortions, attenuation in power spectral estimation. If the probability density function of random jitters is known, then the attenuation can be correctly delineated as a modulation curve which is more severe in higher frequencies. To alleviate attenuation, an ensemble average approach is suggested. It can accurately restore the power spectrum suffered from attenuation due to random jitters. In addition, it can also reliably compute useful statistical parameters of a given random jitter distribution when the statistics is only partially known. Simulation tests were conducted to illustrate the effects of sampling jitters and to demonstrate the effectiveness of this new ensemble average algorithm.