Rayleigh distribution, Random Process and Quantization in Communication Systems In this project, we have three parts.
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Rayleigh Distribution : In the first part, we will review the Rayleigh distribution.
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Random Processes : In the second part, we will analyze a random process to see if it is a Stationary Stochastic Process (WSS). If it's not, we will explore ways to make it a WSS process.
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Quantization : In the third part, we will focus on pulse modulation and work on building a digital transmitter and receiver that can handle noise and decoding.
1-1: Plotting the probability density function (PDF) of the Rayleigh distribution
1-2: Plotting the PDF of two random variables with a Normal distribution having a mean of zero and a variance of one
1-3: Generating and plotting Rayleigh random variable using two normal random variables
1-4: The Impact of Increasing N
When we increase the value of N from 1000 to 100000, the histogram tends to be more accurate because we have a larger number of samples to represent the distribution of the data. With a larger sample size, the histogram bins can capture the underlying distribution more precisely, resulting in a more accurate representation of the data.
2-2: Plotting mean of random process X
2-3: Plotting autocorrelation of random process X
2-4 : Plotting mean and autocorrelation of random process X base on theoretical calculations
2-5 :
We can transform a random process into a wide-sense stationary (WSS) process by taking the mean over time.
3-1 : Definition of continuous signal and sampling and construction of discrete signals
3-3 : Quantization Level Implementation
3-4 : Digital conversion of quantized signals
3-5: Reception of digital signal at the receiver
3-6: Decoding of the digital signal at the receiver
3.7: Conversion of quantized signal back to analog
