102 NATURE PHOTONICS | VOL 7 | FEBRUARY 2013 | www.nature.com/naturephotonics The real-time measurement of fast non-repetitive events is arguably the most challenging problem in the field of instrumentation and measurement1–4. These instruments are needed for investigating rapid transient phenomena such as chemical reactions, phase transitions, protein dynamics in living cells and impairments i...

The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring N by means of an N -slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits N ≈ 10. It is furthermore shown, that sine an...

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh–Fourier series of a function of bounded variation. 2013 Elsevier Inc. All rights reserved.

A novel method for designing a signature based on the conformal mapping is proposed. Conformal mapping function preserves the local angles of the shape of the object. Schwarz Christoffel mapping transformation is effectively implemented. A conformal transformation of the upper half plane onto the interior of a simple polygon is carried out. The widely used in 2-D potential flow for the computat...

A signal processing system was designed to simulate hearing impairment for normal hearing listeners. Typical consequences of sensorineural hearing loss are an elevated threshold in quiet, abnormal growth of loudness ('recruitment') and reduced spectral and temporal resolution. However, the just noticable difference (jnd) in intensity is unaffected. Based on an aurally adequate time-frequency re...

Metamaterials and metastructures with effective relative permittivity near zero exhibit unusual wave properties such as uniform phase distributions across such domains. Here we discuss the possibility of using εnear-zero (ENZ) metamaterials for lensing and Fourier transforming. Owing to the possibility of having ENZ metamaterials in different wavelength regimes, the concepts shown here can be u...

We propose to use photon echoes in rare-earth-doped crystals to implement the Fourier-transform chirp algorithm. The process is considered for application to spectral analysis of fast radio-frequency signals. Compared with surface acoustic wave devices, the proposed scheme gives access to the larger bandwidths of rare-earth-doped crystals and greater flexibility. An experimental demonstration o...

Unknown compounds in environmental samples are difficult to identify using standard mass spectrometric methods. Fourier transform mass spectrometry (FTMS) has revolutionized how environmental analyses are performed. With its unsurpassed mass accuracy, high resolution and sensitivity, researchers now have a tool for difficult and complex environmental analyses. Two features of FTMS are responsib...

Dispersive Fourier transformation (DFT) maps the broadband spectrum of an ultrashort optical pulse into a time stretched waveform with its intensity profile mirroring the spectrum using chromatic dispersion. Owing to its capability of continuous pulse-by-pulse spectroscopic measurement and manipulation, DFT has become an emerging technique for ultrafast signal generation and processing, and hig...

Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the ...