The reconstruction of periodic signals that are embedded in noise is a very important task in many applications. This already difficult task is even more complex when some observations are missed or some are presented irregularly in time. Kolmogorov-Zurbenko (KZ) filtration, a well-developed method, offers a solution to this problem. One section of this paper provides examples of very precise reconstructions of multiple periodic signals covered with high level noise, noise levels that make those signals invisible within the original data. The ability to reconstruct signals from noisy data is applied to the numerical reconstruction of tidal waves in atmospheric pressure. The existence of such waves was proved by well-known naturalist Chapman, but due to the high synoptic fluctuation in atmospheric pressure he was unable to numerically reproduce the waves. Reconstruction of the atmospheric tidal waves reveals a potential intensification on wind speed during hurricanes, which could increase the danger imposed by hurricanes. Due to the periodic structure of the atmospheric tidal wave, it is predictable in time and space, which is important information for the prediction of excess force in developing hurricanes. 1. Introduction The spectral analysis of longitudinal data is the method of analyzing natural periodicities of data that are observed over long periods of time. However, the problem with longitudinal studies is that data is not collected at regular (or equally spaced) time intervals. Studies have been conducted as to how to handle the problem presented by having missing values. Examples of such studies include separating the data into the missing part and the nonmissing part called the EM (Expectation Maximization) algorithm by Shumway and Stoffer [1] and the CLEAN method formulated by Baish and Bokelmann [2], which they tested on simulated noisy data and due to their results applied this method to seismological data. Other researchers have also considered estimating the missing data [3–5]. The Kolmogorov-Zurbenko (KZ) filter is an efficient means of analyzing data even when datasets are considered to have missing values ([6–8], Kolmogorov-Zurbenko filters). Several computer algorithms are available that will investigate a time series with irregularly spaced data, including the nonequispaced Fast Fourier Transform (NFFT) developed by Keiner et al. and the Mathematics Faculty at Chemnitz University of Technology (offered in their free software) and the KZA algorithm provided in R-software by Close and Zurbenko [9]. This paper highlights the strength
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