Forensic analysis of architectural finishes using Fourier transform infrared and Raman spectroscopy, Part I: The resin bases

The ability of Raman spectroscopy and Fourier transform infrared (FT-IR) microscopy to discriminate between resins used for the manufacture of architectural finishes was examined in a study of 39 samples taken from a commercial resin library. Both Raman and FT-IR were able to discriminate between different types of resin and both split the samples into several groups (six for FT-IR, six for Raman), each of which gave similar, but not identical, spectra. In addition, three resins gave unique Raman spectra (four in FTIR). However, approximately half the library comprised samples that were sufficiently similar that they fell into a single large group, whether classified using FT-IR or Raman, although the remaining samples fell into much smaller groups. Further sub-division of the FT-IR groups was not possible because the experimental uncertainty was of similar magnitude to the within-group variation. In contrast, Raman spectroscopy was able to further discriminate between resins that fell within the same groups because the differences in the relative band intensities of the resins, although small, were larger than the experimental uncertainty.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

64-point Fourier transform chip for digital television applications

A 64-point Fourier transform chip is described that performs a forward or inverse, 64-point Fourier transform on complex two's complement data supplied at a rate of 13.5MHz and can operate at clock rates of up to 40MHz, under worst-case conditions. It uses a 0.6µm double-level metal CMOS technology, contains 535k transistors and uses an internal 3.3V power supply. It has an area of 7.8×8mm, dissipates 0.9W, has 48 pins and is housed in a 84 pin PLCC plastic package. The chip is based on a FFT architecture developed from first principles through a detailed investigation of the structure of the relevant DFT matrix and through mapping repetitive blocks within this matrix onto a regular silicon structure.

Bit-level systolic array implementation of the Winograd Fourier transform algorithm

A bit level systolic array system is proposed for the Winograd Fourier transform algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest-neighbor interconnections, regularity and high throughput. The short interconnections in this method contrast favorably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform a short length transform. These components build into longer transforms preserving the regularity and structure of the short length transform design.

A 64-point fourier transform chip for video motion compensation using phase correlation

Details of a new low power fast Fourier transform (FFT) processor for use in digital television applications are presented. This has been fabricated using a 0.6-µm CMOS technology and can perform a 64 point complex forward or inverse FFT on real-time video at up to 18 Megasamples per second. It comprises 0.5 million transistors in a die area of 7.8 × 8 mm and dissipates 1 W. The chip design is based on a novel VLSI architecture which has been derived from a first principles factorization of the discrete Fourier transform (DFT) matrix and tailored to a direct silicon implementation.

SYSTOLIC IMPLEMENTATION OF THE WINOGRAD FOURIER TRANSFORM ALGORITHM.

A bit-level systolic array system is proposed for the Winograd Fourier transform algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest neighbor interconnections, regularity, and high throughput. The short interconnections in this method contrast favorably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform short-length transforms. These components build into longer transforms, preserving the regularity and structure of the short-length transform design.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

Fourier Transform using a Rotman Lens

In this paper, the design constraints that are required for a Rotman lens to realize discrete Fourier transform (DFT) amplitude and phase functionality are derived. A Fourier Rotman lens has been designed, fabricated and validated. The amplitude and phase response and the array pattern based on the CST™ results are validated with the theoretical DFT results. To the best of the authors' knowledge, this is the first Fourier Rotman lens to be fabricated and validated. The solution provided replaces multilayer Butler matrix solutions with a simple single layer microstrip technology.

Forensic analysis of architectural finishes using fourier transform infrared and raman spectroscopy, part II:White paint

White household paints are commonly encountered as evidence in the forensic laboratory but they often cannot be readily distinguished by color alone so Fourier transform infrared (FT-IR) microscopy is used since it can sometimes discriminate between paints prepared with different organic resins. Here we report the first comparative study of FT-IR and Raman spectroscopy for forensic analysis of white paint. Both techniques allowed the 51 white paint samples in the study to be classified by inspection as either belonging to distinct groups or as unique samples. FT-IR gave five groups and four unique samples; Raman gave seven groups and six unique samples. The basis for this discrimination was the type of resin and/ or inorganic pigments/extenders present. Although this allowed approximately half of the white paints to be distinguished by inspection, the other half were all based on a similar resin and did not contain the distinctive modifiers/pigments and extenders that allowed the other samples to be identified. The experimental uncertainty in the relative band intensities measured using FT-IR was similar to the variation within this large group, so no further discrimination was possible. However, the variation in the Raman spectra was larger than the uncertainty, which allowed the large group to be divided into three subgroups and four distinct spectra, based on relative band intensities. The combination of increased discrimination and higher sample throughput means that the Raman method is superior to FT-IR for samples of this type. © 2005 Society for Applied Spectroscopy.