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Dont waste your time and order our essay writing service todaySimulation and Analysis of White Noise in Matlab Gaussian. Waves 3. 0 votes, average 4. Loading. If you are looking for a way to generate AWGN noise in Matlab, go here. Checkout this ebook Digital Modulations using Matlab  by Mathuranathan Viswanathan. White Noise Process. A random process or signal for your visualization with a constant power spectral density PSD function is a white noise process. Power Spectral Density. Power Spectral Density function shows how much power is contained in each of the spectral component. For example, for a sine wave of fixed frequency, the PSD plot will contain only one spectral component present at the given frequency. PSD is an even function and so the frequency components will be mirrored across the Y axis when plotted. Thus for a sine wave of fixed frequency, the double sided plot of PSD will have two components one at ve frequency and another at ve frequency of the sine wave. How to plot PSDFFT in MatlabGaussian and Uniform White Noise A white noise signal process is constituted by a set of independent and identically distributed i. In discrete sense, the white noise signal constitutes a series of samples that are independent and generated from the same probability distribution. For example, you can generate a white noise signal using a random number generator in which all the samples follow a given Gaussian distribution. This is called White Gaussian Noise WGN or Gaussian White Noise. Similarly, a white noise signal generated from a Uniform distribution is called Uniform White Noise. White Gaussian Noise and Uniform White Noise are frequently used in system modelling. In modellingsimulation, a white noise can be generated using an appropriate random generator. White Gaussian Noise can be generated using randn function in Matlab which generates random numbers that follow a Gaussian distribution. Similarly, rand function can be used to generate Uniform White Noise in Matlab that follows a uniform distribution. When the random number generators are used, it generates a series of random numbers from the given distribution. Lets take the example of generating a White Gaussian Noise of length 1. Matlab with zero mean and standard deviation1. More simulation techniques available in this ebook Digital Modulations using Matlab  by Mathuranathan Viswanathan. What is i. i. d This simply generates 1. As we know that a white process is seen as a random process composing several random variables following the same Probability Distribution Function PDF. The 1. 0 random numbers above are generated from the same PDF standard normal distribution. This condition is called identically distributed condition. The individual samples given above are independent of each other. Furthermore, each sample can be viewed as a realization of one random variable. In effect, we have generated a random process that is composed of realizations of 1. Thus, the process above is constituted from independent identically distributed i. Strictly and weakly defined White noise Since the white noise process is constructed from i. PDF. Thus, the Joint Probability Distribution function of the process will not change with any shift in time. This is called a stationary process. Thus the white noise is a stationary process. As with a stationary process which can be classified as Strict Sense Stationary SSS and Wide Sense Stationary WSS processes, we can have white noise that is SSS and white noise that is WSS. Correspondingly they can be called strictly white noise signal and weakly white noise signal. Whats with Covariance FunctionMatrix A white noise signal, denoted by xt, is defined in weak sense is a more practical condition. Here, the samples are statistically uncorrelated and identically distributed with some variance equal to 2. This condition is specified by using a covariance function as. Why do we need a covariance functionBecause, we are dealing with a random process which composes n random variables1. Such a process is viewed as multivariate random vector or multivariate random variable. For multivariate random variables, Covariance function specified how each of the n variables in the given random process behaves with respect to each other. Covariance function generalizes the notion of variance to multiple dimensions. The above equation when represented in the matrix form gives the covariance matrix of the white noise random process. Since the random variables in the white noise process are statistically uncorrelated, the covariance function contains values only along the diagonal. The matrix above indicates that only the auto correlation function exists for each random variable. The cross correlation values are zero samplesvariables are statistically uncorrelated with respect to each other. The diagonal elements are equal to the variance and all other elements in the matrix are zero. The ensemble auto correlation function of the weakly defined white noise is given by This indicates that the auto correlation function of weakly defined white noise process is zero everywhere except at lag tau0. Related topic Constructing the auto correlation matrix in Matlab. Frequency Domain Characteristics Wiener Khintchine Theorem states that for Wide Sense Stationary Process WSS, the power spectral density function Sxxf of the random process can be obtained by Fourier Transform of auto correlation function of the random process. In continuous time domain, this is represented as For the weakly defined white noise process, we find that the mean is a constant and its covariance does not vary with respect to time. This is a sufficient condition for a WSS process. Thus we can apply Weiner Khintchine Theorem. Therefore, the power spectral density of the weakly defined white noise process is constant flat across the entire frequency spectrum. The value of the constant is equal to the variance or power of the white noise. Testing the characteristics of White Gaussian Noise in Matlab Generate a Gaussian white noise signal of length L1. Matlab and plot it. Here the underlying pdf is a Gaussian pdf with mean 0 and standard deviation 2. Thus the variance of the Gaussian pdf is 24. More simulation techniques available in this ebook Digital Modulations using Matlab  by Mathuranathan Viswanathan. L1. 00. 00. 0 Sample length for the random signal. XsigmarandnL,1mu. White noise mux,num. Samples. ylabelSample Values. L1. 00. 00. 0 Sample length for the random signalmu0 sigma2 XsigmaandnL,1mu figure subplot2,1,1plotX titleWhite noise mux,num. SamplesylabelSample Valuesgridon Plot the histogram of the generated white noise and verify the histogram by plotting against the theoretical pdf of the Gaussian random variable. More simulation techniques available in this ebook Digital Modulations using Matlab  by Mathuranathan Viswanathan. Histrogram bins. f,xhistX,n. Theoretical PDF of Gaussian Random Variable. Theoretical PDF and Simulated Histogram of White Gaussian Noise. Histogram,Theoretical PDF. Bins. ylabelPDF fxx subplot2,1,2n1. Histrogram binsf,xhistX,n barx,ftrapzx,f holdon Theoretical. PDFof. Gaussian. Random.