Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A Multi-Mode Sigma-Delta ADC for GSM/WCDMA/ WLAN Applications

The demand for new telecommunication services requiring higher capacities, data rates and different operating modes have motivated the development of new generation multi-standard wireless transceivers. In multistandard design, sigma-delta based ADC is one of the most popular choices. To this end, in this paper we present cascaded 2-2-2 reconfigurable sigma-delta modulator that can handle GSM, WCDMA and WLAN standards. The modulator makes use of a low-distortion swing suppression topology which is highly suitable for wide band applications. In GSM mode, only the first stage (2nd order Σ-Δ ADC) is used to achieve a peak SNDR of 88dB with oversampling ratio of 160 for a bandwidth of 200KHz and for WCDMA mode a 2-2 cascaded structure (4th order) is turned on with 1-bit in the first stage and 2-bit in the second stage to achieve 74 dB peak SNDR with over-sampling ratio of 16 for a bandwidth of 2MHz. Finally, a 2-2-2 cascaded MASH architecture with 4-bit in the last stage is proposed to achieve a peak SNDR of 58dB for WLAN for a bandwidth of 20MHz. The novelty lies in the fact that unused blocks of second and third stages can be made inactive to achieve low power consumption. The modulator is designed in TSMC 0.18um CMOS technology and operates at 1.8 supply voltage

A Triple-Mode Feed-Forward Sigma-Delta Modulator Design For Gsm / Wcdma / Wlan Applications

This paper presents a cascaded 2-2-2 reconfigurable sigma-delta modulator that can handle GSM, WCDMA and WLAN standards. The modulator makes use of a low-distortion swing suppression topology which is highly suitable for wide band applications. In GSM mode, only the first stage (2nd order Σ-Δ ADC) is turned on to achieve 88dB dynamic range with oversampling ratio of 160 for a bandwidth of 200KHz; in WCDMA mode a 2-2 cascaded structure (4th order) is turned on with 1-bit in the first stage and 2-bit in the second stage to achieve 74 dB dynamic range with oversampling ratio of 16 for a bandwidth of 2MHz and a 2-2-2 cascaded MASH architecture with a 4-bit in the last stage to achieve a dynamic range of 58dB for a bandwidth of 20MHz. The novelty lies in the fact that unused blocks of second and third stages can be switched off taking into considerations like power consumption. The modulator is designed in TSMC 0.18um CMOS technology and operates at 1.8 supply voltage.