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 ...

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 ...

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 ...

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.

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 ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are ...

As shown in the last subsection, kernel density estimates can be expressed as a submatrix of a certain convolution. The fast Fourier transform (FFT) is a computationally effective method for computing ...