Question
The first question is to find the phone number that is dialed from a Dual-tone multi-frequency signaling signal. The phone number has six numbers dialed in sequence and matlab file is dialed. Please share the Matlab code and guidelines on how you solved the problem.

The second question is to create M-files that perform the following:
Create an m-file that demonstrates the Law of Large Numbers by taking a uniform random variable from 0 to 10 and show that as the number of samples grows large, the sample average converges to the expected value of the random variable.
Using the MATLAB Histogram function, "hist.m", Illustrate the Central Limit Theorem by taking two different random variables and show how when appropriately scaled and summed, they converge to a Normal (Gaussian) distribution.
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load('525.202-GPS08--3-.mat');
N = length(x)/6;
X = fft(x(1:N));
X = fftshift(X);
f = (-0.5:1/(N-1):0.5)*Fs;
subplot(3,2,1);stem(f,abs(X),'-*k');
title('Magnitude Spectrum of First Number');
xlabel('Frequency(Hz)');

X = fft(x(N+1:2*N));
X = fftshift(X);
f = (-0.5:1/(N-1):0.5)*Fs;
subplot(3,2,2);stem(f,abs(X),'-*k');
title('Magnitude Spectrum of Second Number');
xlabel('Frequency(Hz)');

X = fft(x(2*N+1:3*N));
X = fftshift(X);
f = (-0.5:1/(N-1):0.5)*Fs;
subplot(3,2,3);stem(f,abs(X),'-*k');
title('Magnitude Spectrum of Third Number');
xlabel('Frequency(Hz)');

X = fft(x(3*N+1:4*N));
X = fftshift(X);
f = (-0.5:1/(N-1):0.5)*Fs;
subplot(3,2,4);stem(f,abs(X
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.27mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        1.19mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        Backtrace
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      • select * from `subjects` where `subjects`.`id` in (52)
        1.08mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 51321 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.35mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
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