The Fourier algebra A(G) can be viewed as a dual object for the group G and, in turn, for the group algebra L1(G). It is a commutative Banach algebra constructed using the representation theory of the group, and from which the group G may be recovered as its spectrum. When G is abelian, A(G) coincides with L1(G^); for non-abelian groups, it is viewed as a generalization of this object. B. Johnson has shown that G is amenable as a group if and only if L1(G) is amenable as a Banach algebra. Hence, it is natural to expect that the cohomology of A(G) will reflect the amenability of G. The initial hypothesis to this effect is that G is amenable if and only if A(G) is amenable as a Banach algebra. Interestingly, it turns out that A(G) is amenable only when G has an abelian group of finite index, leaving a large class of amenable groups with non-amenable Fourier algebras. The dual of A(G) is a von Neumann algebra (denoted VN(G)); as such, A(G) inherits a natural operator space structure. With this operator space structure, A(G) is a completely contractive Banach algebra, which is the natural operator space analogue of a Banach algebra. By taking this additional structure into account, one recovers the intuition behind the first conjecture: Z.-J. Ruan showed that G is amenable if and only if A(G) is operator amenable. This thesis concerns both the non-amenability of the Fourier algebra in the category of Banach spaces and why Ruan's Theorem is actually the proper analogue of Johnson's Theorem for A(G). We will see that the operator space projective tensor product behaves well with respect to the Fourier algebra, while the Banach space projective tensor product generally does not. This is crucial to explaining why operator amenability is the right sort of amenability in this context, and more generally, why A(G) should be viewed as a completely contractive Banach algebra and not merely a Banach algebra.

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OFDM (Orthogonal Frequency Division Multiplexing) technology, due to its longer symbol duration that decease the amount of dispersion in time caused by multipath delay spread, has been widely used in many advanced digital communication systems such as DVB (Digital Video Broadcast), WLAN (Wireless Local Area Network), and UWB (Ultra Wide Band). How to realize efficient OFDM systems has been a very important issue for either academic or industry fields in recent years. This thesis aims to explore the VLSI implementation of the OFDM system targeted on its application on the wildly popular IEEE802.11a WLAN systems. An efficient OFDM architecture design involves the algorithm exploration and the tradeoff between the algorithm performance and hardware implementation. Therefore, in this thesis, a Matlab simulation platform for the IEEE802.11a baseband receiver is first built to refine several key synchronization algorithms including frame detection, timing recovery, carrier frequency offset, channel estimation as well as phase tracking under some given channel models. An excellent frame detection and timing recovery method is adopted such that nearly perfect synchronization can be achieved at SNR> 3. Furthermore, area-efficient architecture suitable for VLSI implementation for each synchronization module has also been proposed. In summary, 4 complex multipliers with 388 shift registers are required in our synchronization circuits. These modules are integrated with a core single-path radix-23 IFFT (Inverse Fast Fourier Transform) block to build a highly efficient WLAN baseband.

The Besov class $B_{pq}^s$ is defined by ${ f : { 2^{|n|s}||W_n*f||_p } _{ninmathbb{Z}}in ell^q(mathbb{Z}) }$. When $s=1$, $p=q $, we know if $f in B_p$ if and only if $int_mathbb{D} |f^{(n)}(z)|^p(1-|z|^2)^{2pn-2}dv(z) <+infty$. It is shown in [5] that $int_{mathbb{D}}|f^{'}(z)|^q K(z,z)^{1-q}dv(z)= O(L(b(e^{-(q-p)^{-1}})))$ if $f in B_{L,p}$. In this paper we will show that $f in B_{L,p}$ if and only if $sum_{n=0}^{infty}2^{nq}||W_n*f||_p^q = O(L(b(e^{-(q-p)^{-1}})))$.

¡@¡@A single chip of variable length FFT processor is presented in this thesis. This processor can be applied for the applications with 128/256/512/1024/2048-point FFT. This processor is based on SDF (single path delay feedback) pipeline architecture with radix-2^3 computation element. The number of bits for input data and twiddle factors is carefully selected by system simulation to meet the requirements of OFDM system. In addition, we propose a feedback twiddle factor generator to instead the lookup table for twiddle factors to reduce the storage size of memory. The FFT processor is carried out by CMOS 0.35£gm 2P4M process with core area 3.381x3.3625 mm^2. In the gate level simulation, the output data rate of this FFT processor is above 22.72MHz, so the processor can meet the requirement of IEEE 802.16e standard.

This thesis includes two topics. The first topic is a ZigBee transceiver used in 2.45 GHz band design. The second topic is a 2K/4K/8K multimode fast Fourier transformation ( FFT ) for DVB-H demodulators. The first topic includes simulations and hardware design. The chip is a physical layer design compliant with IEEE Std 802.15.4 standard, including a transmitter and a receiver for 2.45 GHz band. The measurement of the maximum power on silicon is about 731 £gW at 8 MHz. It is proved to be compliant with the low power consumption requirement specified by the standard. The second topic includes simulations and hardware design of an FFT for DVB-H demodulators. This processor is based on a pipeline architecture with radix-2, radix-22 and radix-23 computation element. We propose one sharing butterfly architecture to be used in the variable length FFT processor.

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Thèse de doctorat--Signal et images--Paris--ENST, 2006. / SLM = Spatial light modulator. Bibliogr. p. 123-126. Résumé en français et en anglais.

Thèse de doctorat : Sociologie : Lyon 2 : 2001. / Titre provenant de l'écran-titre. Bibliogr.. Index.

Thesis (M.S.)--Ohio State University, 2009. / Title from first page of PDF file. Includes vita. Includes bibliographical references (p. 51-54).