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Autocorrelation is applied to analyze sets of finite-sampling data such as the turn-by-turn beam position monitor (BPM) data in an accelerator. This method of data analysis, called the independent component analysis (ICA), is shown to be a powerful beam diagnosis tool for being able to decompose sampled signals into its underlying source signals. We find that the ICA has an advantage over the principle component analysis (PCA) used in the model-independent analysis (MIA) in isolating independent modes. The tolerance of the ICA method to noise in the BPM system is systematically studied. The ICA is applied to analyze the complicated beam motion in a rapid-cycling booster synchrotron at the Fermilab. Difficulties and limitations of the ICA method are also discussed.