Digital Communications Chapter 1 Signals and Spectra Signal Processing Lab

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. Digital versus Analog  Advantages of digital Communications: Regenerator receiver

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Digital versus Analog (cont´d)  Advantages of digital Communications: Different kinds of digital signals are treated identically

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. Block Diagram of a DCS (single user)

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. Random Process (cont´d)  Ergodic process : A random process is ergodic in mean and autocorrelation, if

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. Spectral Density  Energy signal : Energy spectral density (ESD) :  Power signal : Power spectral density (PSD)  Random process : Power spectral density (PSD) :

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. 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., Dept. of Elec. and Info. Engr., Korea Univ. Noise in Communication System (cont´d) [ Power spectral density & Autocorrelation function ]

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Signal Transmission through Linear Systems Deterministic signals : Random signals :

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Ideal Pulse

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Signal Transmission through Linear Systems

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Signal Transmission  Ideal filters :

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. Baseband versus Bandpass

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ.

Signal Processing Lab., Dept. of Elec. and Info. Engr., Korea Univ. 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