Extrapolation, Interpolation, and Smoothing of Stationary Time Series

Extrapolation, Interpolation, and Smoothing of Stationary Time Series by Norbert Wiener is a foundational 1949 text that laid the mathematical groundwork for modern signal processing, control theory, and what would become the field of cybernetics.

Originally circulated as a classified MIT Radiation Laboratory report during World War II — nicknamed the "Yellow Peril" by colleagues for its dense yellow cover and formidable mathematics — this work presents Wiener's rigorous treatment of how to optimally predict, filter, and smooth noisy time-series data. Drawing on probability theory and Fourier analysis, Wiener developed what is now known as the Wiener filter, a statistical framework for separating signal from noise that remains central to communications engineering, radar, and data science to this day.

Published commercially in 1949 by MIT Press and John Wiley & Sons, this edition marked the declassification and public release of one of the most mathematically sophisticated wartime research documents ever produced. Wiener, already a towering figure in mathematics at MIT, had developed these methods to solve the practical problem of predicting the flight paths of enemy aircraft for anti-aircraft fire control — a problem that led him to fundamental insights about stochastic processes and feedback systems. The book's publication coincided with Wiener's landmark work Cybernetics (1948) and is considered an essential companion text to understanding the theoretical foundations of the information age.

• First Edition, 1949
• Author: Norbert Wiener