A new algorithm performs Fourier transforms using a minimal number of samples. The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing.

The Odd Discrete Fourier Transform (ODFT) is used in many modern audio codecs which employ the Modified Discrete Cosine Transform (MDCT) for efficient signal representation. The ODFT is used ...

Researchers have developed a new algorithm that, in a large range of practically important cases, improves on the fast Fourier transform. Under some circumstances, the improvement can be dramatic -- a ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...

The discrete cosine transform (DCT) remains a cornerstone of modern image and video compression techniques, enabling the decomposition of visual data into frequency components that can be efficiently ...