We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous Lévy ...

If there's a mathematical idea that applies itself to almost everything in everyday life but is almost unknown outside the scientific world, the Fourier transform has to be the most unsung contender.

The Fourier transform (FT), a cornerstone of optical processing, enables rapid evaluation of fundamental mathematical operations, such as derivatives and integrals. Conventionally, a converging lens ...

Linear transforms — like a Fourier transform — are a key math tool in engineering and science. A team from UCLA recently published a paper describing how they used deep learning techniques to design ...

The Fourier transform is one of the most fundamental concepts in the information sciences. It’s a method for representing an irregular signal — such as the voltage fluctuations in the wire that ...

Typical spectrometers use prisms or diffraction gratings to spread light over a viewing window or digital sensor as a function of frequency. While both prisms and gratings work very well, there are a ...

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure ...

The fast Fourier transform, one of the most important algorithms of the 20th century, revolutionized signal processing. The algorithm allowed computers to quickly perform Fourier ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...