Non-stationarity in an actual wave field restricts the application of the existing methods of estimating spectra. Despite the enormous amount of research work in the past, an analyst today is still faced with the lack of a unique procedure capable of providing a spectrum estimate which can be considered as the most accurate for the wave data collected under conditions where the stationarity assumption is in doubt. In this paper a generalized method is presented for estimating one dimensional frequency spectrum considering the non-stationarity. The generalized method and the associated design relations provide an effective measure for assessing the statistical quality of spectrum estimates, and a natural criterion as to how to select an optimal sample size. Concepts are illustrated by actual wave data analysis* and the validity of the procedure is demonstrated by simulation. In a simple manner, all concepts and methods developed for the non-stationary frequency spectrum apply to the wave number spectrum with spatial inhomogeneity. For simplicity, the presentation here will be primarily directed to the frequency spectrum.