Keywords: binary codes, electrical engineering, engineering

Keywords: Beta, Binomial, Common discrete distributions, Distribution function, Exponential, Gamma, Geometric, Negative binomial, Normal or Gaussian, Poisson, Simple random variable, Symmetric triangular, Uniform, Weibull

Summary: In the unit on Random Variables and Probability, we introduce real random variables as mappings from the basic space to the real line. The mapping induces a transfer of the probability mass on the basic space to subsets of the real line in such a way that the probability that ... that interval. [Expand Summary] In the unit on Random Variables and Probability, we introduce real random variables as mappings from the basic space to the real line. The mapping induces a transfer of the probability mass on the basic space to subsets of the real line in such a way that the probability that X takes a value in a set M is exactly the mass assigned to that set by the transfer. To perform probability calculations, we need to describe analytically the distribution on the line. For simple random variables, we have at each possible value of X a point mass equal to the probability X takes that value. For more general cases, we need a more useful description: the distribution function which at each t has the value of the probability mass at or to the left of t. If the probability mass in the induced distribution is spread smoothly along the real line, with no point mass concentrations, there is a probability density function such that the probability mass in any interval is the area under the curve over that interval. [Collapse Summary]

Keywords: Additivity, Boolean combinations, Classical probability, Events as sets, Freedom at a price, Likelihood, Mutually exclusive, Partitions, Probability mass, Probability measure

Summary: In the module "Likelihood" we introduce the notion of a basic space Ω of all possible outcomes of a trial or experiment; events as subsets of the basic space determined by appropriate characteristics of the outcomes; and logical or Boolean combinations of the events (unions, intersections, and complements) corresponding to ... are derived. [Expand Summary] In the module "Likelihood" we introduce the notion of a basic space Ω of all possible outcomes of a trial or experiment; events as subsets of the basic space determined by appropriate characteristics of the outcomes; and logical or Boolean combinations of the events (unions, intersections, and complements) corresponding to logical combinations of the defining characteristics. Probability is a number assigned to an event indicating the likelihood of the occurrence of that event on any trial. Classical probability: the basic space Ω consists of a finite number N of possible outcomes; each possible outcome is assigned a probability 1/N; if event (subset) A has NA elements, then the probability assigned event A is P(A) = NA/N. Three properties are easily determined; several other elementary properties may be derived from these three. A general probability system consists of a basic set Ω of elementary outcomes of a trial or experiment, a class of events as subsets of the basic space, and a probability measure P which assigns values to the events in accordance with three basic rules from which several other essential rules are derived. [Collapse Summary]

Keywords: BER, bit error rate, conditional probability, constellation diagram, decision regions, erfc, eye diagram, Gray coding, PAM, phase-shift keying, PSK, QAM, Q function, SER, symbol alphabet, symbol error rate

Summary: In this module, we first introduce the eye diagram and constellation diagram as qualitative ways of evaluating the symbol error probability of a digital communication system. We discuss various symbol alphabets, such as QAM, PAM, and PSK, and their associated decision regions. Finally, we derive the symbol error probability for ... Gray coding. [Expand Summary] In this module, we first introduce the eye diagram and constellation diagram as qualitative ways of evaluating the symbol error probability of a digital communication system. We discuss various symbol alphabets, such as QAM, PAM, and PSK, and their associated decision regions. Finally, we derive the symbol error probability for PAM and QAM in additive white Gaussian noise, using the Q and erfc functions, and discuss Gray coding. [Collapse Summary]

Keywords: AM, amplitude modulation, ATSC, carrier tone, Carson's rule, demodulation, discriminator, envelope detection, FM, frequeny modulation, in-phase, large carrier, modulation, NTSC, pilot tone, QAM, quadrature, suppressed carrier, vestigial sideband, VSB

Summary: This module describes basic analog modulation techniques, including amplitude modulation (AM) with suppressed carrier, AM with a pilot tone or carrier tone, quadrature AM (QAM), vestigial sideband modulation (VSB), and frequency modulation (FM). Various demodulation techniques are also discussed, including envelope detection and the discriminator. Application examples include NTSC television ... and stereo). [Expand Summary] This module describes basic analog modulation techniques, including amplitude modulation (AM) with suppressed carrier, AM with a pilot tone or carrier tone, quadrature AM (QAM), vestigial sideband modulation (VSB), and frequency modulation (FM). Various demodulation techniques are also discussed, including envelope detection and the discriminator. Application examples include NTSC television and FM radio (both mono and stereo). [Collapse Summary]