This chapter covers the fundamental principles and current applications of Fourier transform (FT) infrared and Fourier transform Raman spectroscopies as utilized in the analysis of polymeric materials. The primary emphasis of the first part is on the principles and advantages of these interferometric methods, whereas the remaining sections illustrate numerous applications focusing on the struct...

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...

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 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...

Rapid scanning serves to mitigate the problems of scintillation and dynamic range for Fourier spectrometry, as well as to simplify the measurement procedures. Rapid scanning means scanning at a rate such that the interferometric fringes act as their own chopper. It also means scanning at a rate such that the fringe frequencies exceed the scintillation frequencies, thereby avoiding confusion bet...

The methods of fast parallel calculation of multidimensional hypercomplex discrete Fourier transform (HDFT) are discussed. The theoretical and experimental estimation of parallelization efficiency is given. It is shown that proposed method has very high efficiency (up to 90%).

In this paper we introduce convolution theorem for the Fourier transform (FT) of two complex functions. We show that the correlation theorem for the FT can be derived using properties of convolution. We develop this idea to derive the correlation theorem for the quaternion Fourier transform (QFT) of the two quaternion functions.