When last we saw [xoreaxeax], he had built a lens-less optical microscope that deduced the structure of a sample by recording ...

The Fast Fourier Transform allows computers to take complex signals and break them into their underlying frequencies. This single idea makes it possible to analyze sound, images, radio waves, and even ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

A new study finds that a 200-year-old technique called Fourier analysis can reveal crucial information about how the form of artificial intelligence called deep neural networks (DNN) learn to perform ...

Let f(u) be the Fourier-Stieltjes transform of a real or complex-valued function F(α) of bounded variation on (— ∞, ∞). It is shown that if f(u) belongs to L2 on an interval of infinite range, then ...

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.

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 ...

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 ...