Reconstruction of the Primordial Power Spectrum by Direct Inversion

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters.Comment: 23 pages, 9 figure

Multi-user satellite communications system using an innovative compressive receiver

There is a need for an onboard simultaneous multi-channel demodulation system for a satellite communications system. Studies indicate that Convolve Multiply Convolve (CMC) filtering with surface acoustic wave (SAW) dispersive delay lines will eliminate the necessity of onboard satellite channelized filters of complex fourier transform processors. The reason for choosing the CMC technique is its ability to perform Fourier transformations in a shorter time with less space and power consumption than digital Fourier transform processors. Each ground terminal in this multi-users communications system is remotely located and operates independently; hence, a method of synchronizing the transmission of these users is presented which utilizes the existing Global Positioning System (GPS) system. Each ground user is equipped with a low cost ground terminal that has a synchronization subsystem attached to it. The system design of an onboard Multi-channel Receiver and Demodulator utilizes Quadrature Phase Shift Keying (QPSK) as the modulation technique. This technique provides the best figure of merit, i.e., the lowest transmitter power requirement per communication channel

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field