Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections

Abstract

Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.