--The fractional fourier transform(FRFT) which is a generalisation of classical fourier transform, was introduced number of years ago in the mathematics literature but appears to have remained largely unknown to a signal processing community to which it may, however, be a potentially useful. The fractional fourier transform depends on a parameter ‘α’ and can be interpreted as a rotation by an a...

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but di...

We experimentally demonstrate a tunable and reconfigurable optical discrete Fourier transform (DFT) to demultiplex orthogonal-frequency-division-multiplexed subcarriers with 2/3/4 subcarriers at 20/40 GHz frequency spacing. An average power penalty of ~5 dB (~3.5) at bit error ratio of 10(-9) is achieved for 4×20 Gbit/s (4×10 Gbit/s) OFDM signal with 20 GHz frequency spacing.

Time-frequency distributions have been used extensively for nonstationary signal analysis, they describe how the frequency content of a signal is changing in time. The Wigner-Ville distribution (WVD) is the best known. The draw back of WVD is cross-term artifacts. An alternative to the WVD is Gabor transform (GT), a signal decomposition method, which displays the time-frequency energy of a sign...

We report precision measurements by Fourier transform spectroscopy of the vacuum wavenumber, line width, and relative signal strength of 928 lines in the Ar I spectrum. Wavelength in air and classification of the transition are supplied for each line. A comparison of our results with other precision measurements illustrates the sensitivity of Ar I wavelengths to conditions in the light source.

A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) of an input vector. Efficient means that the FFT computes the DFT of an n-element vector in O(n logn) operations in contrast to the O(n2) operations required for computing the DFT by definition. FFTs exist for any vector length n and for real and higher-dimensional data. Parallel FFTs have b...

For the first time, a tunable reflected phase reflectarray is demonstrated in the thermal infrared. This is done using thermochromic VO(2) square-patch elements in a reflectarray metamaterial configuration. A sixty degree change in reflected phase is measured using a Twyman-Green interferometer, and FTIR measurements show that the resonance reflection minima shifts from 9.2 to 11.2 mum as the s...

We propose a new approach to broadband Stimulated Raman Scattering (SRS) spectroscopy and microscopy based on time-domain Fourier transform (FT) detection of the stimulated Raman gain (SRG) spectrum. We generate two phase-locked replicas of the Stokes pulse after the sample using a passive birefringent interferometer and measure by the FT technique both the Stokes and the SRG spectra. Our appro...