frequency content of the process. Ensemble averaging and Time averaging can be used to obtain the process properties Ensemble averaging Properties of the process are obtained by averaging over a collection or ensemble of sample records using values at corresponding times Time averaging Properties are obtained by averaging over a single record in time Stationary random processes A random process is said to be stationary if its statistical characterization is independent of the observation interval over which the process was initiated. Ensemble averages do not vary with time. An ensemble of random processes is said to be stationary if and only if its probability distributions pn depend only on time differences, not on absolute time pn yn tn y2 t2 y1 t1 pn yn tn y2 t2 y1 t1 If this property holds for the absolute probabilities pn. Most stationary random processes can be treated as ergodic. A random process is ergodic if every member of the process carries with it the complete statistics of the whole process. Then its ensemble averages will equal appropriate time averages. Of necessity, an ergodic process must be stationary, but not all stationary processes are ergodic.
Nonstationary random processes Nonstationary random processes arise when one is studying a system whose evolution is influenced by some sort of clock that cares about absolute time. For example, the speeds v t of the oxygen molecules in downtown Logan, Utah make up an ensemble of random processes regulated in part by the rotation of the earth and the orbital motion of the earth around the sun and the influence of these clocks makes v t be a nonstationary random process. By contrast, stationary random processes arise in the absence of any regulating clocks. An example is the speeds v t of oxygen molecules in a room kept at constant temperature.
Amplitude modulation 2.1
Modulation is a process of varying one of the characteristics of high frequency sinusoidal the carrier in accordance with the instantaneous values of the modulating the information signal. The high frequency carrier signal is mathematically represented by the equation 2.1. c t Ac cos 2 f c t Where c t --instantaneous values of the cosine wave