Covariance-invariant signal processing

Chapter 9 - Discrete-Time Signals and Systems

A novel method is presented for the exact design and synthesis of lossless discrete-integrator (LDI) digital filters. In this method, the entire digital filter synthesis is performed directly in the discrete-time z-domain without any recourse to the concept of a continuous-time analog prototype reference filter. The proposed design method lends itself in a straightforward fashion to the synthesis of high-quality LDI digital filters having ladder, lattice, or other similar practical configurations. In addition, it is capable of realizing a wide class of practical digital transfer functions, including the classical Butterworth Chebyshev, inverse Chebyshev, and, most importantly, elliptic transfer functions. >

A novel framework for retiming using evolutionary computation for high level synthesis of digital filters

Genetic algorithms are exploited and applied to the development of a novel approach to the high-level synthesis of digit-serial digital filters. The salient feature of this approach is that it permits the digit-size to be taken into account as a variable of optimization, facilitating global data-path optimization with respect to both area and time. Moreover, it conforms closely to an actual hardware implementation, taking into account not only the cost of the required arithmetic functional units but also that of the required registers and multiplexors. The proposed approach is particularly efficient as it preserves the data-dependency relationships in the original digital filter data flow-graph under the operations of crossover and mutation performed by the constituent genetic algorithm. The effectiveness of this approach is demonstrated by comparing its results to those obtained by using the existing techniques for the high-level synthesis of a benchmark wave digital filter implemented as a bit-parallel architecture, and by presenting the results for the corresponding digital filter implemented as a digit-serial architecture.

We present the experimental application and comparison of two methods for the synthesis of digital filters, which represent the state-of-the-art of optimum digital processing of shaped signals with arbitrary constraints in time and frequency domain and any kind of stationary noise power spectral density. The methods are implemented in experimental measurement setups and optimum filters are synthesized with regard to assigned constraints (e.g. finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system, identified from datasets of straightforward signal experimental acquisitions. Implementation issues are detailed and design rules for digital signal processors based on these techniques are derived.

As the complexity of digital filters is dominated by the number of multiplications, many works have focused on minimizing the complexity of multiplier blocks that compute the constant coefficient multiplications required in filters. The complexity of multiplier blocks can be significantly reduced by using an efficient number system. Although the canonical signed digit representation is commonly used as it guarantees the minimal number of additions for a constant multiplication, we propose in this paper a digital filter synthesis algorithm that is based on the minimal signed digit (MSD) representation. The MSD representation is attractive because it provides a number of forms that have the minimal number of non-zero digits for a constant. This redundancy can lead to efficient filters if a proper MSD representation is selected for each constant. In experimental results, the proposed algorithm resulted in superior filters to those generated from the CSD representation.

Methods of digital signal processing in control and monitoring systems are relevant today and largely replace the classic analog methods. This article discusses the main methods of digital signal processing and synthesis of appropriate devices, primarily digital filters.

This study is an integral part of a project focusing on the synthesis of IIR digital filters with finite word length. The implementation of the project involves considering the finite word length already at the stage of computation zeros and poles. The results of this stage are final and are not distorted at the stage of structural synthesis. The computation uses the fact that the zeros and poles of a practically implemented digital filter are elements of the set of algebraic numbers of the corresponding degree. At the stage of structural synthesis, a digital filter block diagram is generated. This block diagram provides specified degrees of algebraic numbers, which are zeros and poles. The exact values of the coefficients of the generated digital filter structure are calculated taking into account previously calculated zeros and poles. Different structures are characterized by structural precision, independent of specific coefficient values. This paper is devoted to the study of the generation of structures that provide a given structural precision of the denominator of the transfer function and a given degree of algebraic numbers that are poles.

ECG is the main tool used by the physicians for identifying and for interpretation of Heart condition. The ECG should be free from noise and of good quality for the correct diagnosis. In real time situations ECG are corrupted by many types of artifacts. The high frequency noise is one of them. The present paper deals with removing of noise from ECG of high frequency contents with help of Low pass digital filter of the cutoff frequency 100Hz. The sampling period used is .001sec. The filter is designed with Butterworth Approximations. The results of before filtration and after filtration are depicted in the paper. Paper contains detail design of the digital Butterworth filter and its realization. The experimentation is performed on the database generated in Laboratory. The simulation results show the filter works satisfactorily with some modifications in PQRST waveform.

This work presents the methodology utilized for the development of the numerical module of SIPREX, an expert system for digital filter design. This system integrates knowledge on the different techniques and application areas of digital signal processing with powerful numerical algorithms, representing a valuable tool for the solution of problems involving analysis and synthesis of digital filters.

Chapter 1 - Continuous-Time Signals

In this paper, the problem of sampling a continuous-time generalized almost-cyclostationary (GACS) signal is addressed. The class of such nonstationary signals includes, as a special case, the almost-cyclostationary (ACS) signals. ACS signals filtered by some linear time-variant channels are further examples. It is shown that the discrete-time signal constituted by the samples of a GACS signal is a discrete-time ACS signal. Thus, the nonstationarity kind of a continuous-time GACS signal cannot be deducted from that of the discrete-time signal of its samples. However, in the paper it is shown how, starting from the sampled signal, the GACS or ACS nature of the continuous-time signal can be conjectured, provided that analysis parameters such as sampling period, padding factor, and data-record length are properly chosen.

We present the experimental application and comparison of two methods for the synthesis of digital filters, which represent the state-of-the-art of optimum digital processing of shaped signals with arbitrary constraints in time and frequency domain, and any kind of stationary noise power spectral density. The methods are implemented in experimental measurement setups, and optimum filters are synthesized with regard to assigned constraints (e.g., finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system, identified from datasets of simple signal experimental acquisitions. Implementation issues are detailed and basic design rules for digital signal processors based on these techniques are derived.

It is commonly assumed that digital filters with both poles and zeros in the complex z-plane can be synthesized using only recursive techniques while filters with zeros alone can be synthesized by either direct convolution or via the discrete Fourier transform (DFT). In this letter it is shown that no such restrictions hold and that both types of filters (those with zeros alone or those with both poles and zeros) can be synthesized using any of the three methods, namely, recursion, DFT, or direct convolution.

The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.