1. Create the random noise using the following command that ensures v has the sa
ID: 1834752 • Letter: 1
Question
1. Create the random noise using the following command that ensures v has the same size as x:a. v=randn(size(x))
2. Using a solid line style, plot the first 1000 points of v vs. time and notice the erratic time characteristics of the noise.
3. Compute the DFT of the first 4096 points of the noise and plot the noise’s DFT magnitude in dB vs. frequency. Notice that the noise DFT magnitude is “flat” (well, it is quite ragged, but the top of the plot is flat), which is why this kind of noise is called “white” noise – it consists of equal amounts of all frequencies just like white light consists of equal amounts of all colors.
Explanation / Answer
White noise is a random signal (or process) with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency. White noise draws its name from white light in which the power spectral density of the light is distributed over the visible band in such a way that the eye's three color receptors (cones) are approximately equally stimulated. In statistical sense, a time series rt is characterized as having weak white noise if {rt} is a sequence of serially uncorrelated random variables with zero mean and finite variance. Strong white noise also has the quality of being independent and identically distributed, which implies no autocorrelation. In particular, if rt is normally distributed with mean zero and standard deviation s , the series is called a Gaussian white noise.[1] An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. A random signal is considered "white noise" if it is observed to have a flat spectrum over a medium's widest possible bandwidth.
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