Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel

Application of multirate digital signal processing to image compression

With the increasing emphasis on digital communication and digital processing of images and video, image compression is drawing considerable interest as a means of reducing computer storage and communication channels bandwidth requirements. This thesis presents a method for the compression of grayscale images which is based on the multirate digital signal processing system. The input image spectrum is decomposed into octave wide subbands by critically resampling and filtering the image using separable FIR digital filters. These filters are chosen to satisfy the perfect reconstruction requirement. Simulation results on rectangularly sampled images (including a text image) are presented. Then, the algorithm is applied to the hexagonally resampled images and the results show a slight increase in the compression efficiency. Comparing the results against the standard (JPEG), indicate that this method does not have the blocking effect of JPEG and it preserves the edges even in the presence of high noise level

A Compressive Phase-Locked Loop

We develop a new method for tracking narrowband signals acquired through compressive sensing, called the compressive sensing phase-locked loop (CS-PLL). The CS-PLL enables one to track oscillating signals in very large bandwidths using a small number of measurements. Not only does the CS-PLL potentially operate below the Nyquist rate, it can extract phase and frequency information without the computational complexity normally associated with compressive sensing signal re-construction. The CS-PLL has a wide variety of applications, including but not limited to communications, phase tracking, robust control, sensing, and FM demodulation. In particular we emphasize the advantages of using this system in wideband surveillence systems. Our design modifies classical PLL designs to operate with CS-based sampling systems. Performance results are shown for PLLs operating on both real and complex data. In addition to explaining general performance tradeoffs, implementations using several different CS sampling systems are explored

Randomized sampling and multiplier-less filtering

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 151-153).This thesis considers the benefits of randomization in two fundamental signal processing techniques: sampling and filtering. The first part develops randomized non-uniform sampling as a method to mitigate the effects of aliasing. Randomization of the sampling times is shown to convert aliasing error due to uniform under-sampling into uncorrelated shapeable noise. In certain applications, especially perceptual ones, this form of error may be preferable. Two sampling structures with are developed in this thesis. In the first, denoted simple randomized sampling, non-white sampling processes can be designed to frequency-shape the error spectrum, so that its power is minimized in the band of interest. In the second model, denoted filtered randomized sampling, a pre-filter, post-filter, and the sampling process can be designed to further frequency-shape the error to improve performance. The thesis develops design techniques using parametric binary process models to optimize the performance of randomized non-uniform sampling. In addition, a detailed second-order error analysis, including performance bounds and results from simulation, is presented for each type of sampling. The second part of this thesis develops randomization as a method to improve the performance of multiplier-less FIR filters. Static multiplier-less filters, even when carefully designed, result in frequency distortion as compared to a desired continuous-valued filter. Replacing each static tap with a binary random process is shown to mitigate this distortion, converting the error into uncorrelated shapeable noise. As with randomized sampling, in certain applications this form of error may be preferable. This thesis presents a FIR Direct Form I randomized multiplier-less filter structure denoted binary randomized filtering (BRF). In its most general form, BRF incorporates over-sampling combined with a tapped delay-line that changes in time according to a binary vector process.(cont)The time and tap correlation of the binary vector process can be designed to improve the error performance. The thesis develops design techniques using parametric binary vector process models to do so. In addition, a detailed second-order error analysis, including performance bounds, error scaling with over-sampling, and results from simulation, is presented for the various forms of BRF.by Sourav R. Dey.Ph.D

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Spectrally and Energy Efficient Wireless Communications: Signal and System Design, Mathematical Modelling and Optimisation

This thesis explores engineering studies and designs aiming to meeting the requirements of enhancing capacity and energy efficiency for next generation communication networks. Challenges of spectrum scarcity and energy constraints are addressed and new technologies are proposed, analytically investigated and examined. The thesis commences by reviewing studies on spectrally and energy-efficient techniques, with a special focus on non-orthogonal multicarrier modulation, particularly spectrally efficient frequency division multiplexing (SEFDM). Rigorous theoretical and mathematical modelling studies of SEFDM are presented. Moreover, to address the potential application of SEFDM under the 5th generation new radio (5G NR) heterogeneous numerologies, simulation-based studies of SEFDM coexisting with orthogonal frequency division multiplexing (OFDM) are conducted. New signal formats and corresponding transceiver structure are designed, using a Hilbert transform filter pair for shaping pulses. Detailed modelling and numerical investigations show that the proposed signal doubles spectral efficiency without performance degradation, with studies of two signal formats; uncoded narrow-band internet of things (NB-IoT) signals and unframed turbo coded multi-carrier signals. The thesis also considers using constellation shaping techniques and SEFDM for capacity enhancement in 5G system. Probabilistic shaping for SEFDM is proposed and modelled to show both transmission energy reduction and bandwidth saving with advantageous flexibility for data rate adaptation. Expanding on constellation shaping to improve performance further, a comparative study of multidimensional modulation techniques is carried out. A four-dimensional signal, with better noise immunity is investigated, for which metaheuristic optimisation algorithms are studied, developed, and conducted to optimise bit-to-symbol mapping. Finally, a specially designed machine learning technique for signal and system design in physical layer communications is proposed, utilising the application of autoencoder-based end-to-end learning. Multidimensional signal modulation with multidimensional constellation shaping is proposed and optimised by using machine learning techniques, demonstrating significant improvement in spectral and energy efficiencies

MMSE design of interpolation and downsampling FIR filters in the context of periodic nonuniform sampling

The generalized sampling theorem states that any analog signal whose spectrum is limited to 1/T can be exactly recovered from N sequences of samples taken at a rate 2/NT and all having a different sampling phase, When N = 2, the exact interpolation formula can be derived quite easily. The ideal interpolation filters have infinite impulse responses (IIR's), This paper addresses first the question of recovering front the two initial sequences any other sequence taken at the same rate 1/T and with a different sampling phase, The design problem is dealt with for finite length filters, and the criterion is the minimization of the mean squared interpolation error, Next, the problem of computing from the two initial sequences a third one at a lower rate is addressed, FIR decimation filters are also designed for an MMSE criterion, These problems are illustrated for two typical covariance functions

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement