{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/algebraic-data-analysis","title":"Applications of the discrete-time Fourier transform to data analysis","arxiv_id":null,"date":"2023-07-08","proceeding":"International Journal of Data Science and Analytics 2023 7","authors":["dayne sorvisto"],"abstract":"We define a discrete analogue of the characteristic function for discrete random variable and develop numerical procedures for computing the discrete characteristic function for several well-known discrete random variables. We rigorously define what is meant by the Fourier transform of a probability mass function and also show how to reverse the process to recover the probability mass function of a discrete random variable, given a procedure for computing the characteristic function. Unlike previous work on the subject, our approach is novel in that we are not computing closed-form solutions of a continuous random variable but are focused on applying the methods to real-world data sets.","url_abs":"https://link.springer.com/article/10.1007/s41060-023-00409-5","url_pdf":"https://rdcu.be/dgoqU","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"computing-characateristic-functions","task_name":"Computing Characateristic Functions"}],"methods":[{"method_slug":"characteristic-functions","method_name":"Characteristic Functions"}],"datasets_introduced":[],"methods_introduced":[{"slug":"characteristic-functions","name":"Characteristic Functions","full_name":"Characteristic Function Estimation for Discrete Probability Distributions"}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}