Final answer:
Using MATLAB's 'randn' and 'rand' functions, we can calculate the percentage of amplitudes falling within specific ranges of Gaussian and uniform noise and plot histograms to illustrate the distribution differences, with Gaussian noise exhibiting central clustering and uniform noise showing even distribution.
Step-by-step explanation:
To address the question of creating a Gaussian noise with 2000 samples and analyzing the distribution of its amplitudes, we utilize MATLAB's randn function for Gaussian distribution and rand for uniform distribution. The identified ranges specify intervals in which we calculate the percentage of samples that fall within each one, using logical indexing to filter out the values in those ranges and then computing the ratio with respect to the total sample size.
For the uniform distribution, the analysis is similar; however, we expect the distribution of percentages among the given ranges to be more uniform compared to the Gaussian noise, as the probability density function of a uniform distribution is flat, whereas that of the Gaussian distribution has a bell-shaped curve, with a higher concentration of values around the mean and fewer as we move farther from it.
A histogram is plotted using hist with 20 bins for both types of noise, allowing us to visualize the frequency of sample values within each bin. The major difference expected between the two histograms is the shape of the distribution, specifically the uniformity in the case of uniform distributed noise versus the central clustering in Gaussian noise.