Table Of Contents



How to search for terms and topics covered in this website? One option is the Find tool of your web browser.

Find the Control key (Command key on Mac). While holding that key down, also press the F key. A find box will open, and you can enter a word to locate it on the page. Where exactly the find box opens on your screen varies, depending on which browser you use.

Please note the following: 1) The find tool can be used on only one page at a time. 2) At this time, there is no easy way to use Control-F/ Command-F to find two words near each other if they are not adjacent.


Because the treatment of the subject offered by this website is both deep and broad, it behooves the user to take full advantage of Page 1, “Home”, before delving into the more technical subjects of each of the twelve following pages. The next step should ideally be a non-superficial study of Page 2, “Learning About Cyclostationarity” which is the core of the website. For the deepest understanding of the theory of cyclostationarity, the next priority should be Page 3, which provides the most comprehensive comparison of the two alternative theories of cyclostationarity available in the literature. The following priority should probably be Page 4, “Extending the Cyclostationarity Paradigm . . .” because this opens the door to understanding how to apply the theory of cyclostationarity when time-series data exhibits only irregular cyclostationarity, not regular cyclostationarity.  Such time series data frequently arise in the natural sciences where irregular cyclicity is a common occurrence. After studying these four pages in sequence, the order in which the remaining eight pages are studied is up to the user’s particular interests or priorities. Scholars and historians may find much material of interest on Pages 6 through 10 and 12 and some sections on Page 11. Researchers looking for opportunities to contribute to further developments of the theory and associated methodology may find Page 11 stimulating.


Feedback on experience with using this website for self-education can be sent to the Website Content Manager (WCM) by using the link at the bottom center of each page. When appropriate and otherwise possible, the WCM will try to reply to feedback including submitted questions.


Professor Gardner challenges users of this website to find and report any technical errors that are more than just a typographical error, though reports of any typographical errors found also will be appreciated. Professor Gardner has already made his best effort at proofreading the website content, and his previous graduate student, Grace Yeung, has added to his effort. So, any successful challenges will be considered a contribution, and he will—when possible—acknowledge any substantive technical errors found at the website.


If you think a first-year graduate-level college/university course on Fraction-of-Time Probability models for time series data and/or on cyclostationary time-series analysis–which does not have a prerequisite of a course on the more abstract topic of stochastic processes–would be desirable, please submit your thoughts about this to the WCM, and indicate whether your thoughts come from the perspective of a student or a faculty member or a scientific data analyst or signal processing engineer working in the field. 


For brief overviews of the extensive base of scientists and engineers who have contributed to the growth the field of study that this website is devoted to, see Pages 6 and 12. The seminal contributions which have made this growth possible are summarized on Page 9. Other historical remarks are scattered throughout the website.


There have been forces that have worked against the paradigm shift promoted by this website—authors of publications that either disagree with the claimed superior utility, for many applications, of the FOT-Probability theory of cyclostationarity, relative to the more abstract Stochastic Process theory, or ignore the very existence of the alternative FOT-Probability theory. The detrimental effects of these resisting forces are exposed throughout this website, with particular focus given on Page 3 and, from a more general perspective relevant to the advancement of Science in general, on Page 7.