DCOM_3_Random process1.pptx
- 2. RANDOM SIGNALS ▫ Signals can be divided into two main categories - deterministic and random. The term random signal is used primarily to denote signals, which have a random in its nature source. As an example we can mention the thermal noise, which is created by the random movement of electrons in an electric conductor. ▫ The term random signal is used also for signals falling into other categories, such as periodic signals, which have one or several parameters that have appropriate random behavior. ▫ An example is a periodic sinusoidal signal with a random phase or amplitude. Signals can be treated either as deterministic or random, depending on the application. Speech, for example, can be considered as a deterministic signal, if one specific speech waveform is considered. It can also be viewed as a random process if one considers the ensemble of all possible speech waveforms in order to design a system that will optimally process speech signals, in general. 2
- 3. 3 Random signals can be both analog and digital. The values of digital signals are represented with a finite number of digits. This implies that the stochastic terms used are different for the two signal categories.
- 4. 4 Random variables- In the study of probability, any process of observation is referred to as an experiment. The results of an observation are called outcomes of the experiment. If the outcomes of an experiment cannot be predicted, then it is called random experiment. The set of possible outcomes of a random experiment is called the sample space. An element in the sample space is called a sample point. Each outcome of a random experiment corresponds to a sample point. Subsets of the sample space are called events, and events consisting of a single element (sample point) are called elementary events.
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- 19. 19 Random Variables A variable is something which can change its value. It may vary with different outcomes of an experiment. If the value of a variable depends upon the outcome of a random experiment it is a random variable. A random variable can take up any real value. Mathematically, a random variable is a real-valued function whose domain is a sample space S of a random experiment. A random variable is always denoted by capital letter like X, Y, M etc. The lowercase letters like x, y, z, m etc. represent the value of the random variable.
- 20. 20 Consider the random experiment of tossing a coin 20 times. You will earn Rs. 5 is you get head and will lose Rs. 5 if it a tail. You and your friend are all set to see who will win the game by earning more money. Here, we see that the value of getting head for the coin tossed for 20 times is anything from zero to twenty. If we denote the number of a head by X, then X = {0, 1, 2, … , 20}. The probability of getting a head is always ½.
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