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Digital Communications

Digital Communications. Chapter 1 Signals and Spectra Signal Processing Lab. Digital Communication System (DCS). Important features of a DCS Transmitter sends a waveform from a finite set of possible waveforms during a limited time

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Digital Communications

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  1. Digital Communications Chapter 1 Signals and Spectra Signal Processing Lab

  2. Digital Communication System (DCS) • Important features of a DCS • Transmitter sends a waveform from a finite set of possible waveforms during a limited time • Receiver decides which waveform was transmitted from the noisy received signal • Probability of erroneous decision is an important measure for the system performance Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  3. Digital versus Analog • Advantages of digital Communications: • Regenerator receiver Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  4. Digital versus Analog (cont´d) • Advantages of digital Communications: • Different kinds of digital signals are treated identically Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  5. Digital versus Analog(cont´d) • Advantages of digital Communications • More robust to distortion and interference • Digital circuits are more reliable and cheaper • Digital hardwares are more flexible in implementation • Suitable for digital terminals like computers • Disadvantages of digital Communications • Intensive signal processing • Synchronization problems • Non-graceful degradation Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  6. Block Diagram of a DCS (single user) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  7. Some Basic Concepts and Definitions in DCS • Classification of signals • Deterministic or random • Periodic or non-periodic • Analog or discrete • Power or energy • Random process • Autocorrelation • Power and energy spectral densities • Noise in communications systems • Signal transmission through linear systems • Bandwidth of signal Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  8. Classification of Signals • Deterministic and random signals • Deterministic signal : No uncertainty with respect to the signal value at any time • Random signal : Some degree of uncertainty in signal values before it actually occurs • Thermal noise in electronic circuits due to the random movement of electrons • Reflection of radio waves from different layers of ionosphere Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  9. Classification of Signals (cont´d) • Periodic and non-periodic signals • Periodic signal : A signal is called periodic if there exist a constant such that • The smallest value of satisfying this condition, is called the period of Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  10. Classification of Signals (cont´d) • Analog and Discrete signals • Analog signal is a continuous function of time. • Discrete signal exists only at discrete values of time Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  11. Classification of Signals (cont´d) • Energy and power signals • Energy signal : is classified as an energy signal if, and only if, it has nonzero but finite energy for all time, where • Power signal : is defined as a power signal if, and only if, it has finite but nonzero power for all time where • General rule : Periodic and random signals are power signal. Signals that are both deterministic and non-periodic are Energy signals Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  12. Random Process • A random process is a collection of time function, or signals, corresponding to various outcomes of random experiment. For each outcome, , there exists a deterministic function, which is called a sample function or a realization Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  13. Random Process (cont´d) • Strictly stationary : If none of the statistics of the random process are affected by a shift in the time origin • Wide sense stationary (WSS): If the mean and autocorrelation function do not change with a shift in the time origin • Cyclostationary : If the mean and autocorrelation are periodic in time with some period Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  14. Random Process (cont´d) • Ergodic process : A random process is ergodic in mean and autocorrelation, if Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  15. Autocorrelation • Autocorrelation of an energy signal • Autocorrelation of a power signal • For a periodic signal : • Autocorrelation of a random signal • For a WSS process : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  16. Spectral Density • Energy signal : • Energy spectral density (ESD) : • Power signal : • Power spectral density (PSD) • Random process : • Power spectral density (PSD) : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  17. Properties of an Autocorrelation Function • For real-valued and WSS random signals : • Autocorrelation and spectral density form a Fourier transform pair. • Autocorrelation is symmetric around zero. • Its maximum value occurs at the origin • Its value at the origin is equal to the average power or energy. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  18. Noise in Communication System • Thermal noise is described by a zero-mean Gaussian random process, n(t) • Its PSD is flat, hence, it is called white noise. [Probability density function] Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  19. Noise in Communication System (cont´d) [ Power spectral density & Autocorrelation function ] Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  20. Signal Transmission through Linear Systems • Deterministic signals : • Random signals : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  21. Ideal Pulse Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  22. Signal Transmission through Linear Systems Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  23. Signal Transmission • Ideal filters : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  24. Baseband versus Bandpass Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  25. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  26. Bandwidth of Signal (cont´d) • Different definition of bandwidth a) Half-power bandwidth d) Fractional power containment bandwidth b) Noise equivalent bandwidth e) Bound power spectral density c) Null-to-null bandwidth f) Absolute bandwidth Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

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