| Some applications of the Discrete Fourier Transform (DFT) in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in general commutative rings. I. The (Usual) Discrete Fourier Transform Let be a primitive N th root of uni...

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationsh...

The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...

لایه کَندگی کربن‌­چگالی‌­بالا یکی از گزینه‌­های امیدبخش در افروزش گرماهسته­‌ای هدف­‌های گداخت محصورشدگی لختی است. به منظور کاهش ناپایداری‌­های هیدرودینامیکی و هم‌­چنین حفظ سوخت پدیده پیش‌­گرمایش، طراحی دوتایی با بیرونی کربن­‌چگالی­‌بالا که اخیراً توسط محققین مورد توجه قرار گرفته است، استفاده شده این‌­رو این پژوهش، بهینه‌­سازی یک هدف کروی دلخواه تک پلی‌­استایرن را کد MULTI-IFE بررسی دادیم. هدف، تح...

PURPOSE The purpose of this study was to assess the relationship between baseline caries experience and the restoration replacement rate in children. METHODS The 5-year New England Children's Amalgam Trial recruited 534 6- to 10-year-old children with 2 or more carious posterior teeth. The association between decoy and longevity of restorations was assessed. Restorations with no follow-up (N ...