The need to measure high repetition rate ultrafast processes cuts across multiple areas of science. last decade has seen tremendous advances in the development and application new techniques this field, as well many breakthrough achievements analyzing non-repetitive optical phenomena. Several approaches now provide convenient access single-shot waveform characterization, including dispersive Fo...

Time-frequency concentration operators restrict the integral analysis-synthesis formula for short-time Fourier transform to a given compact domain. We estimate how much corresponding eigenvalue counting function deviates from Lebesgue measure

The Fourier transform is one of the most fundamental tools for computing the frequency representation of signals. It plays a central role in signal processing, communications, audio and video compression, medical imaging, genomics, astronomy, as well as many other areas. Because of its widespread use, fast algorithms for computing the Fourier transform can benefit a large number of applications...