Deterministic Discrete-Time Signal Transforms

2021 ◽  
pp. 714-796
Author(s):  
Stevan Berber
Keyword(s):  
Fourier Transform ◽  
Discrete Time ◽  
Linear Time ◽  
Power Spectra ◽  
Time Signal ◽  
Linear Time Invariant ◽  
Energy Spectral Density ◽  
Analysis And Synthesis ◽  
Spectral Density Functions ◽  
Linear Time Invariant Systems

Chapter 15 presents a detailed analysis of discrete-time signals and systems in the frequency domain, including the theory of the discrete Fourier series, the discrete-time Fourier transform, and the discrete Fourier transform, and key examples relevant for the analysis and synthesis of signals processed in the discrete transceiver blocks of a communication system. Amplitude spectra, magnitude spectra, phase spectra, and power spectra are defined and calculated for typical signals. Using a unique notation that distinguishes between energy signals and power signals, the correlation function and power or energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of linear-time-invariant systems, using the notions of impulse responses, correlation functions, and power spectral densities for both power and energy signals, is presented. The basic theory of the z-transform is also presented.

Deterministic Continuous-Time Signals and Systems

2021 ◽  
pp. 562-598
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Continuous Variable ◽  
Linear Time Invariant ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
Linear Time Invariant Systems ◽  
Definition Of ◽  
Time Invariant

Due to the importance of the concept of independent variable modification, the definition of linear-time-invariant system, and their implications for discrete-time signal processing, Chapter 11 presents basic deterministic continuous-time signals and systems. These signals, expressed in the form of functions and functionals such as the Dirac delta function, are used throughout the book for deterministic and stochastic signal analysis, in both the continuous-time and the discrete-time domains. The definition of the autocorrelation function, and an explanation of the convolution procedure in linear-time-invariant systems, are presented in detail, due to their importance in communication systems analysis and synthesis. A linear modification of the independent continuous variable is presented for specific cases, like time shift, time reversal, and time and amplitude scaling.

Deterministic Discrete-Time Signals and Systems

2021 ◽  
pp. 690-713
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Communication Systems ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Discrete Signals ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
Linear Time Invariant Systems ◽  
Definition Of ◽  
Time Invariant

Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic discrete-time signals and systems. These discrete signals, which are expressed in the form of functions, including the Kronecker delta function and the discrete rectangular pulse, are used throughout the book for deterministic discrete signal analysis. The chapter also presents the definition of the autocorrelation function and the explanation of the convolution procedure in linear-time-invariant systems for discrete-time signals in detail, due to the importance of these in the analysis and synthesis of discrete communication systems.

scholarly journals Interval Estimation Methods for Discrete-Time Linear Time-Invariant Systems

2019 ◽  
Vol 64 (11) ◽  
pp. 4717-4724 ◽  
Author(s):  
Wentao Tang ◽  
Zhenhua Wang ◽  
Ye Wang ◽  
Tarek Raissi ◽  
Yi Shen
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Interval Estimation ◽  
Estimation Methods ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Time Linear

Transforms of Deterministic Continuous-Time Signals

2021 ◽  
pp. 599-673
Author(s):  
Stevan Berber
Keyword(s):  
Spectral Density ◽  
Continuous Time ◽  
Communication Systems ◽  
Fourier Transforms ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Energy Spectral Density ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
The Fourier Transform

Chapter 12 presents a detailed analysis of continuous-time signals and systems in the frequency domain, including the theory of Fourier series and Fourier transforms, and key examples relevant for the analysis and synthesis of signals processed in the digital transceiver blocks of a communication system. The amplitude, magnitude, phase, and power spectra are defined and calculated for typical signals. In particular, the Fourier transform of periodic signals is presented, due to its importance in communication systems theory and practice. Using a unique notation that distinguishes energy and power signals, the correlation, power, and energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of a linear-time-invariant system, using the concepts of impulse response, system correlation function, and power spectral density, both for power signals and energy signals, is presented. In addition, Parseval’s theorem and the Rayleigh theorem are proven.

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