The Springer Series in Information Sciences, edited by T.S. Huang, includes volumes on content-addressable memories, fast Fourier transform and convolution algorithms, pitch determination of speech signals, and pattern analysis. Volume 2, "Fast Fourier Transform and Convolution Algorithms," by H. J. Nussbaumer, focuses on the implementation of digital filters and the evaluation of discrete Fourier transforms using fast algorithms. The book is structured into eight chapters, covering background information on number theory and polynomial algebra, fast convolution algorithms, the fast Fourier transform, linear filtering computation of discrete Fourier transforms, polynomial transforms, and number-theoretic transforms. It aims to provide a unified approach to these techniques, using polynomial algebra to clarify the relationships between different algorithms and suggest improved computation methods. The book also includes practical applications and comparisons with conventional FFT methods, making it a valuable resource for researchers and practitioners in the field of digital signal processing.The Springer Series in Information Sciences, edited by T.S. Huang, includes volumes on content-addressable memories, fast Fourier transform and convolution algorithms, pitch determination of speech signals, and pattern analysis. Volume 2, "Fast Fourier Transform and Convolution Algorithms," by H. J. Nussbaumer, focuses on the implementation of digital filters and the evaluation of discrete Fourier transforms using fast algorithms. The book is structured into eight chapters, covering background information on number theory and polynomial algebra, fast convolution algorithms, the fast Fourier transform, linear filtering computation of discrete Fourier transforms, polynomial transforms, and number-theoretic transforms. It aims to provide a unified approach to these techniques, using polynomial algebra to clarify the relationships between different algorithms and suggest improved computation methods. The book also includes practical applications and comparisons with conventional FFT methods, making it a valuable resource for researchers and practitioners in the field of digital signal processing.