Cyclic LTI systems in digital signal processing

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Multi-dimensional filter design in digital television systems

Imperial Users onl

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

The role of lossless systems in modern digital signal processing: a tutorial

A self-contained discussion of discrete-time lossless systems and their properties and relevance in digital signal processing is presented. The basic concept of losslessness is introduced, and several algebraic properties of lossless systems are studied. An understanding of these properties is crucial in order to exploit the rich usefulness of lossless systems in digital signal processing. Since lossless systems typically have many input and output terminals, a brief review of multiinput multioutput systems is included. The most general form of a rational lossless transfer matrix is presented along with synthesis procedures for the FIR (finite impulse response) case. Some applications of lossless systems in signal processing are presented

Low complexity and efficient dynamic spectrum learning and tunable bandwidth access for heterogeneous decentralized cognitive radio networks

International audienceThis paper deals with the design of the low complexity and efficient dynamic spectrum learning and access (DSLA) scheme for next-generation heterogeneous decentralized Cognitive Radio Networks (CRNs) such as Long Term Evolution-Advanced and 5G. Existing DSLA schemes for decentralized CRNs are focused predominantly on the decision making policies which perform the task of orthogonalization of secondary users to optimum vacant subbands of fixed bandwidth. The focus of this paper is the design of DSLA scheme for decentralized CRNs to support the tunable vacant bandwidth requirements of the secondary users while minimizing the computationally intensive subband switchings. We first propose a new low complexity VDF which is designed by modifying second order frequency transformation and subsequently combining it with the interpolation technique. It is referred to as Interpolation and Modified Frequency Transformation based VDF (IMFT-VDF) and it provides tunable bandpass responses anywhere over Nyquist band with complete control over the bandwidth as well as the center frequency. Second, we propose a tunable decision making policy, ρt_randρt_rand, consisting of learning and access unit, and is designed to take full advantage of exclusive frequency response control offered by IMFT-VDF. The simulation results verify the superiority of the proposed DSLA scheme over the existing DSLA schemes while complexity comparisons indicate total gate count savings from 11% to as high as 87% over various existing schemes. Also, lower number of subband switchings make the proposed scheme power-efficient and suitable for battery-operated cognitive radio terminals