Fourier analysis provides a powerful framework for decomposing functions into sums or integrals of sinusoidal components, thereby enabling the study of frequency content in signals. In tandem, ...

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 ...

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 ...

Wavelets provide new capabilities for analyzing real-time signals. This introductory article provides an overview and presents the basic mechanisms involved in wavelets. In many signal processing ...

Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionised science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves ...

The representation of a periodic sound or waveform as a sum of Fourier components (i.e. pure sinusoidal waves). According to the Fourier theorem, periodic sound may be shown to consist of sine waves ...

Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous ...

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 ...

The Miracle software package has been developed specifically for the IR5 spectrometer with a focus on smooth workflow and ease of use. Miracle regulates each aspect of the experiment, from instrument ...

Fourier Transform Near-Infrared (FT-NIR) Spectrometers are used to identify and characterize chemicals and compounds in a test sample. These devices are based on the characteristic absorption or ...