Analysis of protein sequences can avoid many problems inherently existing in the study of nucleotide sequences given the knowledge that DNA sequences contain all the information for regulating protein expression. This paper presents a spectral approach for calculating the similarity of protein sequences, which can be useful for the inferences of protein functions. The proposed method is based on the mathematical concepts of linear predictive coding and cepstral distortion measure. We show that this spectral approach can reveal non-trivial results from an experimental study of a set of functionally related and functionally non-related protein sequences, and has advantages over some existing approaches.