Sampling and Reconstruction of Continuous-Time Signals

2021 ◽  
pp. 674-689
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Communication Systems ◽  
Digital Signal ◽  
Time Signal ◽  
Reconstruction Filter ◽  
Analogue To Digital ◽  
Sampling And Reconstruction ◽  
The Mathematical Model ◽  
Time Form

This chapter presents the theory for transferring a continuous-time signal into its discrete-time form by sampling, and then converting the obtained samples to a digital signal suitable for processing in a processing machine, using the procedure of sample quantizing and coding. Then, the procedure of converting a digitally processed signal into discrete signal samples and the reconstruction of the initial continuous-time signal via a lowpass reconstruction filter is presented. The theory provides the mathematical base for both analogue-to-digital and digital-to-analogue conversions, which are extensively used for processing signals in discrete communication systems. The chapter goes on to show that the Nyquist criterion must be fulfilled to eliminate signal aliasing in the frequency domain. Finally, the mathematical model for transferring a continuous-time signal into its discrete-time form, and vice versa, is presented and demonstrated for a sinusoidal signal.

scholarly journals Combination of HP and LP filters for narrow band antialiasing filter

2021 ◽  
Vol 72 (4) ◽  
pp. 283-286
Author(s):  
Bohumil Brtník
Keyword(s):  
Signal Processing ◽  
Discrete Time ◽  
Operational Amplifier ◽  
Narrow Band ◽  
Time Signal ◽  
Spice Simulation ◽  
Output Resistance ◽  
High Frequencies ◽  
Filter Structure ◽  
Reconstruction Filter

Abstract The discrete time signal processing requires an anti-aliasing filter at the input and a reconstruction filter at output. Some filters of biquads structure are characterized by a decreasing of the attenuation at high frequencies, caused by the final value of the output resistance of the operational amplifier. In this paper we discuss a design of combined BP filter without mentioned decrease. The proposed filter structure was verified by SPICE simulation.

Digital Filters

2011 ◽  
pp. 180-196
Author(s):  
Gordana Jovanovic-Dolecek
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Digital Filters ◽  
Time Signal ◽  
Digital Signals ◽  
Video Signals ◽  
Time Signals ◽  
Time Distance ◽  
Independent Variable ◽  
Distance Position

A signal is defined as any physical quantity that varies with changes of one or more independent variables, and each can be any physical value, such as time, distance, position, temperature, or pressure (Oppenheim & Schafer, 1999; Elali, 2003; Smith, 2002). The independent variable is usually referred to as “time”. Examples of signals that we frequently encounter are speech, music, picture, and video signals. If the independent variable is continuous, the signal is called continuous-time signal or analog signal, and is mathematically denoted as x(t). For discrete-time signals the independent variable is a discrete variable and therefore a discrete-time signal is defined as a function of an independent variable n, where n is an integer. Consequently, x(n) represents a sequence of values, some of which can be zeros, for each value of integer n. The discrete–time signal is not defined at instants between integers and is incorrect to say that x(n) is zero at times between integers. The amplitude of both the continuous and discrete-time signals may be continuous or discrete. Digital signals are discrete-time signals for which the amplitude is discrete. Figure 1 illustrates the analog and the discrete-time signals.

Discrete-time singularly perturbed Markov chains: aggregation, occupation measures, and switching diffusion limit

2003 ◽  
Vol 35 (2) ◽  
pp. 449-476 ◽  
Author(s):  
G. Yin ◽  
Q. Zhang ◽  
G. Badowski
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Communication Systems ◽  
Large Scale ◽  
Optimization Problems ◽  
Singularly Perturbed ◽  
Diffusion Limit ◽  
Switching Diffusion ◽  
Occupation Measures

This work is devoted to asymptotic properties of singularly perturbed Markov chains in discrete time. The motivation stems from applications in discrete-time control and optimization problems, manufacturing and production planning, stochastic networks, and communication systems, in which finite-state Markov chains are used to model large-scale and complex systems. To reduce the complexity of the underlying system, the states in each recurrent class are aggregated into a single state. Although the aggregated process may not be Markovian, its continuous-time interpolation converges to a continuous-time Markov chain whose generator is a function determined by the invariant measures of the recurrent states. Sequences of occupation measures are defined. A mean square estimate on a sequence of unscaled occupation measures is obtained. Furthermore, it is proved that a suitably scaled sequence of occupation measures converges to a switching diffusion.

Correction of (sin x)/x distortion introduced by discrete-time/continuous-time signal conversion

1988 ◽  
Vol 24 (25) ◽  
pp. 1559 ◽  
Author(s):  
J.C.M. Bermudez ◽  
R. Seara ◽  
S. Noceti Filho
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Time Signal ◽  
Signal Conversion

Fundamentals of Fourier Analysis

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Transform ◽  
Discrete Time ◽  
Continuous Time ◽  
Fourier Integral ◽  
Time Signal ◽  
Continuous Sampling ◽  
Common Reference ◽  
Multidimensional Signals ◽  
Time Signals ◽  
The Fourier Transform

This chapter contains foundational material for modelling of signals and systems. Section 2.2 introduces classes of functions useful in signal processing and analysis. The Fourier transform, in Section 2.3, begins with the Fourier integral and develops the Fourier series, the discrete time Fourier transform and the discrete Fourier transform as special cases. The following material in this chapter can be skipped on a first reading. † denotes material relevant to multidimensional signals in Chapters 8 and 11. ‡ denotes material relevant to probability and stochastic processes in Chapter 4. ¶ denotes material used in continuous sampling in Chapter 10. There are a number of signal classes to which we will make common reference. Continuous time signals are denoted with their arguments in parentheses, e.g., x(t). Discrete time signals will be bracketed, e.g., x[n]. A continuous time signal, x(t), is periodic if there exists a T such that x(t) = x(t − T) for all t. The function x(t) = constant is periodic. A discrete time signal, x[n], is periodic if there exists a positive integer N such that x[n] = x[n − N] for all n. The function x[n] = constant is periodic.

Discrete Communication Systems

2021 ◽  
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Communication Systems ◽  
Linear Time ◽  
General Structure ◽  
Systems Design ◽  
Theory And Practice ◽  
Time Signal ◽  
Linear Time Invariant ◽  
Special Cases ◽  
Gaussian Density

The book present essential theory and practice of the discrete communication systems design, based on the theory of discrete time stochastic processes, and their relation to the existing theory of digital communication systems. Using the notion of stochastic linear time invariant systems, in addition to the orhogonality principles, a general structure of the discrete communication system is constructed in terms of mathematical operators. Based on this structure, the MPSK, MFSK, QAM, OFDM and CDMA systems, using discrete modulation methods, are deduced as special cases. The signals are processed in the time and frequency domain, which requires precise derivatives of their amplitude spectral density functions, correlation functions and related energy and pover spectral densities. The book is self-sufficient, because it uses the unified notation both in the main ten chapters explaining communications systems theory and nine supplementary chapters dealing with the continuous and discrete time signal processing for both the deterministic and stochastic signals. In this context, the indexing of vital signals and finctions makes obvious distinction beteween them. Having in mind the controversial nature of the continuous time white Gaussian noise process, a separate chapter is dedicated to the noise discretisation by introducing notions of noise entropy and trauncated Gaussian density function to avoid limitations in applying the Nyquist criterion. The text of the book is acompained by the solutions of problems for all chapters and a set of deign projects with the defined projects’ topics and tasks and offered solutions.

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