Sinusoidal Frequency Estimation with Nonuniform Samples

Abstract

Frequency estimation of signals is an important topic in the spectral analysis, which is useful in many applications, such as astronomy, bioinformatics, biomedical engineering and audio processing. There exists many frequency estimators for uniformly sampled signals, but the signal samples may be irregularly-spaced in real applications, such as the periodogram analysis of unevenly sampled gene expression data. Therefore, frequency estimation method was developed for irregularly-spaced sinusoids in the presence of additive white Gaussian noise in this project. Four frequency estimators were implemented for uniformly-sampled sinusoids initially, and their performances were compared by performing computer simulations in MATLAB. It was found that the Maximum Likelihood Estimator (MLE) has the best performance, when the noise level was small and the signal length was long enough. The MLE was then derived to deal with irregularly-spaced samples, so it can be applied to non-uniformly sampled gene expression data, as an application of spectral estimation in bioinformatics. The algorithm proposed was used to rank the periodicity of the data. In conclusion, it had acceptable performance on identifying periodic genes, but may be further improved to produce better result.