![]() This equation also works for 2 N, … k N period. The fundamental period N 0 is the smallest period value where this equation works. The periodic discrete-time signals x nwith the period N, where N is the positive integer number, are characterised by the feature x n = x n + Nfor all nvalues. a, b – the time shift transformation for continuous-time and discrete-time signals c, d – reverse transformation for continuous-time and discrete-time signals e, f – scale transformation for continuous-time and discrete-time signals. For discrete-time variables the transformations are the same x n → x a n + b .įigure 1 depicts different kinds of signal transformations for continuous-time and discrete-time variables. Here the transformation depends on the value and sign of numbers, so if a > 0 and a > 1 the signal is extended, if a > 0 and a < 1 the signal is compressed, if a < 0 , the signal is reversed and can be extended or compressed, depending on the bmagnitude and sign of the signal is shifted right or left. Transformation x ( t ) → x ( a t + b ), is where a and b are given numbers.For continuous-time signals x ( – t ) is a x ( t ) reflection over t = 0. Time reversal is when the signal x – n is obtained from x n by reflecting the signal relatively – n = 0.The same for time-continuous signals x ( t ) and x ( t – t 0 ). Time shift is the transformation when two signals x n and x n – n 0 are the same but are displaced relatively to each other.We are considering here the most simple and frequent variable transformations that can be combined, resulting in complex transformations. The parentheses ( t 1, t 2 ) can be used for describing the time-continuous interval t 1 0. Here the brackets are describing the time-continuous interval t 1 ≤ t ≤ t 2. Here x ( t ) is the magnitude of the function x ( t ). The total energy of the continuous-time signal x ( t )over the interval t ∈ t 1, t 2 is ∫ t 1 t 2 | x ( t ) | 2 d t. The signals we are describing are obviously related to the features of the system as power and energy. The feature of the discrete-time signals is that they are sampling continuous-time signals. Also the independent variable is enclosed at parentheses for continuous-time signals and to the brackets for discrete-time systems. Usually the variable indicates the continuous time signals, and the variable n indicates the discrete-time system. Discrete-time signals are defined at the discrete moment of time and the mathematical function takes the discrete set of values.Ĭontinuous-time signals are characterised by independent variables that are continuous and define a continuous set of values. There are two types of signals – discrete-time and continuous-time signals. This post answers the question “What is the difference between continuous and discrete signal?” From a general point of view, signals are functions of one or several independent variables. ![]()
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