Unified Theory for Biorthogonal Modulated Filter Banks

Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

Algorithms and architectures for the multirate additive synthesis of musical tones

In classical Additive Synthesis (AS), the output signal is the sum of a large number of independently controllable sinusoidal partials. The advantages of AS for music synthesis are well known as is the high computational cost. This thesis is concerned with the computational optimisation of AS by multirate DSP techniques. In note-based music synthesis, the expected bounds of the frequency trajectory of each partial in a finite lifecycle tone determine critical time-invariant partial-specific sample rates which are lower than the conventional rate (in excess of 40kHz) resulting in computational savings. Scheduling and interpolation (to suppress quantisation noise) for many sample rates is required, leading to the concept of Multirate Additive Synthesis (MAS) where these overheads are minimised by synthesis filterbanks which quantise the set of available sample rates. Alternative AS optimisations are also appraised. It is shown that a hierarchical interpretation of the QMF filterbank preserves AS generality and permits efficient context-specific adaptation of computation to required note dynamics. Practical QMF implementation and the modifications necessary for MAS are discussed. QMF transition widths can be logically excluded from the MAS paradigm, at a cost. Therefore a novel filterbank is evaluated where transition widths are physically excluded. Benchmarking of a hypothetical orchestral synthesis application provides a tentative quantitative analysis of the performance improvement of MAS over AS. The mapping of MAS into VLSI is opened by a review of sine computation techniques. Then the functional specification and high-level design of a conceptual MAS Coprocessor (MASC) is developed which functions with high autonomy in a loosely-coupled master- slave configuration with a Host CPU which executes filterbanks in software. Standard hardware optimisation techniques are used, such as pipelining, based upon the principle of an application-specific memory hierarchy which maximises MASC throughput

Wavelets and Subband Coding

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

Anthropomorphic Coding of Speech and Audio: A Model Inversion Approach

Auditory modeling is a well-established methodology that provides insight into human perception and that facilitates the extraction of signal features that are most relevant to the listener. The aim of this paper is to provide a tutorial on perceptual speech and audio coding using an invertible auditory model. In this approach, the audio signal is converted into an auditory representation using an invertible auditory model. The auditory representation is quantized and coded. Upon decoding, it is then transformed back into the acoustic domain. This transformation converts a complex distortion criterion into a simple one, thus facilitating quantization with low complexity. We briefly review past work on auditory models and describe in more detail the components of our invertible model and its inversion procedure, that is, the method to reconstruct the signal from the output of the auditory model. We summarize attempts to use the auditory representation for low-bit-rate coding. Our approach also allows the exploitation of the inherent redundancy of the human auditory system for the purpose of multiple description (joint source-channel) coding

Software Defined Radio using MATLAB & Simulink and the RTL-SDR

The availability of the RTL-SDR for less than $20 brings SDR to the home and work desktops of EE students, professional engineers and the maker community. The RTL-SDR device can be used to acquire and sample RF (radio frequency) signals transmitted in the frequency range 25MHz to 1.75GHz, and using some official software add-ons, these samples can be brought into the MATLAB and Simulink environment for users to develop receivers using first principles DSP algorithms. Signals that the RTL-SDR hardware can receive include: FM radio, UHF band signals, ISM signals, GSM, 3G and LTE mobile radio, GPS and satellite signals, and any that the reader can (legally) transmit of course! In this free book we introduce readers to SDR methods by viewing and analysing downconverted RF signals in the time and frequency domains, and then provide extensive DSP enabled SDR design exercises which the reader can learn from. The hands-on examples begin with simple AM and FM receivers, and move on to the more challenging aspects of PHY layer DSP, where receive filter chains, real-time channelisers, and advanced concepts such as carrier synchronisers, digital PLL designs and QPSK timing and phase synchronisers are implemented. Towards the end of the book, we demonstrate how the RTL-SDR can be used with SDR transmitters to develop a more complete communications system, capable of transmitting text strings and images across the desktop

Waveform Design for 5G and beyond Systems

5G traffic has very diverse requirements with respect to data rate, delay, and reliability. The concept of using multiple OFDM numerologies adopted in the 5G NR standard will likely meet these multiple requirements to some extent. However, the traffic is radically accruing different characteristics and requirements when compared with the initial stage of 5G, which focused mainly on high-speed multimedia data applications. For instance, applications such as vehicular communications and robotics control require a highly reliable and ultra-low delay. In addition, various emerging M2M applications have sparse traffic with a small amount of data to be delivered. The state-of-the-art OFDM technique has some limitations when addressing the aforementioned requirements at the same time. Meanwhile, numerous waveform alternatives, such as FBMC, GFDM, and UFMC, have been explored. They also have their own pros and cons due to their intrinsic waveform properties. Hence, it is the opportune moment to come up with modification/variations/combinations to the aforementioned techniques or a new waveform design for 5G systems and beyond. The aim of this Special Issue is to provide the latest research and advances in the field of waveform design for 5G systems and beyond

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github