"Higher order cumulants and spectra have found a variety of uses in many areas of digital signal processing. The third order spectrum, or bispectrum, is of specific interest to researchers because of some of its properties. The Bispectrum is defined as the fourier transform of the third order cumulant se quence for stochastic processes, and as a triple product of fourier transforms for deterministic signals. In the past, bispectral analysis has been used in applications such as identification of linear filters, quadratic phase coupling problems and detection of deviations from normality. This work is aimed at developing techniques for reconstructing deterministic signals in noise us ing the bispectrum. The bispectrum is zero for many noise processes, and is insensitive to linear phase shifts. The main motivation of this work is to exploit these properties of bispectrum that are potentially useful in signal re covery. The existing bispectral recovery techniques are discussed in the signal reconstruction frame work and their main limitation in handling noisy de terministic signals is brought out. New robust reconstruction procedures are provided in order to use bispectrum in such cases. The developed algorithms are tested over a range of simulated applications to bring out their robustness in handling both deterministic and stochastic signals. The new techniques are compared with existing bispectral methods in various problems. This thesis also discusses some of the tradeoffs involved in using bispectrum based reconstruction approaches against non-bispectral methods."--Abstract.
By studying applications in radar, telecommunications and digital image restoration, this monograph discusses signal processing techniques based on bispectral methods. Improved robustness against different forms of noise as well as preservation of phase information render this method a valuable alternative to common power-spectrum analysis used in radar object recognition, digital wireless communications, and jitter removal in images.
By studying applications in radar, telecommunications and digital image restoration, this monograph discusses signal processing techniques based on bispectral methods. Improved robustness against different forms of noise as well as preservation of phase information render this method a valuable alternative to common power-spectrum analysis used in radar object recognition, digital wireless communications, and jitter removal in images.
This book highlights key technologies of signal processing in pulsar-based navigation. It discusses the modeling, simulation, acquisition, and correction of relativistic effects of signals from X-ray pulsars. It demonstrates the methods of contour reconstruction and denoising, and introduces the concept and methods of the average contour. The performance of the phase measurement methods using signal contour is analyzed. The role of wavelets and bispectral methods in the denoising of pulsar signals is discussed. The measurements of pulsar signals’ arriving time are looked into from the perspective of time series. The book is intended for researchers and engineers interested in pulsar-based navigation. It is also a good reference source for senior undergraduates and postgraduate students majoring in navigation and signal processing.
With coherent mixing in the optical domain and processing in the digital domain, advanced receiving techniques employing ultra-high speed sampling rates have progressed tremendously over the last few years. These advances have brought coherent reception systems for lightwave-carried information to the next stage, resulting in ultra-high capacity global internetworking. Digital Processing: Optical Transmission and Coherent Receiving Techniques describes modern coherent receiving techniques for optical transmission and aspects of modern digital optical communications in the most basic lines. The book includes simplified descriptions of modulation techniques for such digital transmission systems carried by light waves. It discusses the basic aspects of modern digital optical communications in the most basic lines. In addition, the book covers digital processing techniques and basic algorithms to compensate for impairments and carrier recovery, as well as noise models, analysis, and transmission system performance.
This manual will be valuable to practicing engineers who need an introduction to polyspectra from a signal processing perspective. In response to the recent growth of interest in polyspectra, this timely text provides an introduction to signal processing methods that are based on polyspectra and cumulants concepts. The emphasis of the book is placed on the presentation of signal processing tools for use in situations where the more common power spectrum estimation techniques fall short.
Signals collected with spherical geometry appear in a large number and diverse range of real-world applications in various disciplines, such as geophysics, medical imaging, computer graphics, wireless communications and acoustics. This thesis focuses on the development of signal processing techniques for sampling and reconstruction of signals on the sphere. The objective of developing new spherical signal measurement and reconstruction techniques is driven by meeting the practical requirements of applications where signals are inherently defined on the sphere. The first part of this thesis develops novel sampling schemes on the sphere for the applications of measuring and reconstructing the head-related transfer function (HRTF) in acoustics and the diffusion signal in diffusion magnetic resonance imaging (dMRI). In contrast to existing sampling schemes in the literature, the developed schemes attain the optimal number of samples, equal to the degrees of freedom in spherical harmonic space, while enabling computation of the spherical harmonic transform (SHT) to near machine precision accuracy. In addition, the proposed sampling schemes have computationally efficient algorithms for the computation of the SHT and are designed to satisfy all the practical requirements of their applications. The proposed scheme for HRTF measurement and reconstruction has non-dense sampling near the poles and is iso-latitude, allowing for the measurements to be more easily obtained. Furthermore, the proposed scheme can be configured as fully hierarchical which enables the HRTF to be analyzed at all frequencies in the audible range using the same arrangement of speakers (or microphones). Numerical experiments and simulations are conducted to demonstrate the reconstruction accuracy of the proposed sampling scheme. Two sampling schemes are proposed for the measurement and reconstruction of the diffusion signal in dMRI which exploit the antipodal symmetry of the diffusion signal in the spatial and spectral domains respectively to attain an optimal number of samples. In addition, the reconstruction accuracy of both schemes does not change significantly with rotation. The spectral antipodal sampling scheme has slightly greater reconstruction accuracy and smaller storage requirements, while the spatial antipodal sampling scheme is more similar to the schemes used by the dMRI community. The second part of the thesis develops signal processing techniques for signal reconstruction in the Slepian basis. Slepian functions must be computed numerically, and therefore inexactly, for arbitrary regions on the sphere. An analytical formulation is developed for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region which enables exact computation. The formulation is extended for an arbitrary region comprised of a union of rotated limited colatitude-longitude subregions. In addition, a computationally efficient algorithm for the implementation of the proposed analytical formulation is developed. Computational complexity analysis is performed and examples provided to illustrate the use of the algorithm in applications. A new method for the computation of Slepian functions on the sphere for an arbitrary spatial region is proposed. Computing Slepian functions with large band-limits is infeasible using the conventional method. The proposed method enables faster computation and has smaller memory storage requirements while maintaining accurate computation, enabling the computation of Slepian functions with larger band-limits.
