29/6/2024 Updated

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture10_Example Codes/Lec9_Ex1.m

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+% Write a code for computing energy and power of x(t) = exp(-t)*unit_step(t)
+% and decide whether x(t) is energy/power signal or not. 
+
+clear all; close all; clc;
+% syms t  T
+% % x = exp(-t).*unit_step(t);
+% x = exp(-t).*heaviside(t);
+% E = int(abs(x).^2,-inf,inf)
+% P = limit((1/T)*int(abs(x)^2,0,T),T,inf)
+fprinf('');
+
+% Write a code for computing energy and power of x(t) = 0.25^n.*unit_step(t)
+% and decide whether x(t) is energy/power signal or not. 
+
+clear all; close all; clc;
+syms n  T
+x = 0.25^n.*heaviside(n);
+E =double( int(abs(x).^2,-inf,inf))
+P = limit((1/T)*int(abs(x)^2,0,T),T,inf)
+fprinf('');

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture10_Example Codes/Lec9_Ex2.m

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+% Generate and plot the pdf of uniform variables
+clear all; close all; clc;
+
+% Generate 10^6 datas with uniform distribution from 0 to 1
+x = 2*rand(1,10^6)-1;
+% x = (b-a)*rand(1,L) + a; % Generate L uniform distributed variables from the range [a, b];
+% Use histogram to get the plot of distribution
+nbins = 100;
+histogram(x,nbins)
+[h, x_axis_vec] = hist(x,nbins);
+area = trapz(x_axis_vec,h);
+% 2/nbins*sum(h)
+pdf = h/area;
+figure
+bar(x_axis_vec,pdf)
+ylim([0 0.6]); xlim([-1.2,1.2])

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture10_Example Codes/ramp.m

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+% This sub-function code is to represent the ramp function
+% ramp(t) is t if t >=0 and, otherwise, is 0.
+function result = ramp(t)
+    result = t.*(t>=0);
+%     result = t.*unit_step(t);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture10_Example Codes/rect.m

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+% This sub-function code is to represent the rectangular function
+% rect(t) is 1/T if -T/2 <= t <= T/2 and, otherwise, is 0.
+function result = rect(t,T)
+    result = 1/T*((t>=-T/2)&(t <= T/2));
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture10_Example Codes/unit_step.m

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+% This sub-function code is to represent the unit-step function
+% u(t) is 1 if t >=0 and, otherwise, is 0.
+function result = unit_step(t)
+    result = 1.*(t>=0);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture1_Example_Code/Ex1.m

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+% This code is to compute 1+2+...+n
+clc; clear all; close all;
+n = 5;
+x = 0;
+for i = 1:n
+    i
+    x = x+i;
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture1_Example_Code/Ex2.m

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+% Input the value and display the value
+clc; clear all; close all;
+
+x = input('Enter the value of x = ');
+disp('The value of x is: ');
+disp(x);
+

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture1_Example_Code/Ex3.m

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+% Array and Matrices
+clc; clear all; close all; 
+
+% Dealing with complex vector
+z = [i; 1+2i; 1-i]
+z'      % transpose with conjugate for complex numbers
+z.'     % transpose without conjugate for complex numbers
+conj(z) % not transpose but conjugate for complex numbers
+
+% Take or replace elements from matrices 
+x = zeros(2,3)
+x = ones(2,3)
+
+x = 1:2:20
+x(1:2:length(x))
+fliplr(x)
+x([1, 5])
+
+
+

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/Lec4_Ex1.m

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+clc; clear all; close all;
+
+x = -4:4;
+[r, m] = func_ex_1(x)

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/Lec4_Ex2.m

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+% Test the convergence
+clc; clear all; close all;
+% Code the RHS 
+N_vec = 1:15; f_N_vec = zeros(1,length(N_vec));
+for ind = 1:length(N_vec)
+    N = N_vec(ind);
+    f_N = lec4_func_ex2(N);
+    f_N_vec(ind) = f_N;
+end
+% Code the LHS
+y_LHS = pi*ones(1,length(N_vec));
+% Plot
+figure
+plot(N_vec, f_N_vec)
+hold on; grid on;
+plot(N_vec, y_LHS,'x');
+
+
+

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/Lec4_Ex3.m

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+% Redo Example 2 with the cumsum in sub-function
+clc; clear all; close all;
+% RHS
+N = 10;
+y_RHS = lec4_func_ex3(N);
+% LHS
+y_LHS = pi*ones(1,length(y_RHS));
+
+% Plot
+x_axis_vec = 0:N;
+figure
+plot(x_axis_vec, y_RHS)
+hold on; grid on;
+plot(x_axis_vec, y_LHS,'x');
+
+
+

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/Lec4_Ex4.m

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+% Do the example 4 in Lecture 4.
+clc; clear all; close all;
+x_vec = 0:0.01:4;
+N=10;
+k= 0:N;
+
+f_x_vec = zeros(1,length(x_vec));
+for ind = 1:length(x_vec)
+    x = x_vec(ind);
+    f_x = (4./pi)*sum(sin(x.*(2.*k+1))./(2.*k+1));
+    f_x_vec(ind) = f_x;
+end
+plot(x_vec,f_x_vec)

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/fib.m

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+% Recursive Functions of Fibonacci: f(n)=f(n-1)+f(n-2)
+
+function y = fib(n)
+   if n == 1
+       y = 0;   % Create first initial value of Fib
+   end
+   if n == 2
+       y = 1;   % Create second initial value of Fib
+   end
+   if n > 2
+       y = fib(n-1) + fib(n-2);
+   end
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/func_ex_1.m

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+% Write a sub-function to calculate the 
+% RMS value and the mean-absolute value
+
+function [rms_val, mean_val] = func_ex_1(x)
+   rms_val = sqrt(sum(abs(x).^2)/length(x));
+   mean_val = sum(abs(x))/length(x);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/lec4_Ex5.m

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+clc; clear all; close all;
+
+y = [];
+for n = 1:10
+    y = [y fib(n)];
+end
+y

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/lec4_func_ex2.m

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+function result = lec4_func_ex2(N)
+   k_vec = 0:N;
+   x_vec = ((-1/3).^k_vec)./(2*k_vec+1);
+   result = 2*sqrt(3)*sum(x_vec);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture4_Example Codes/lec4_func_ex3.m

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+function result = lec4_func_ex3(N)
+   k_vec = 0:N;
+   x_vec = ((-1/3).^k_vec)./(2*k_vec+1);
+   result = 2*sqrt(3)*cumsum(x_vec);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture5_Example Codes/indi_func.m

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+function result = indi_func(x_vec,a,b)
+    result = (x_vec >= a)&(x_vec < b);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture5_Example Codes/lec5_ex1.m

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+% Practice to use indicator functions
+clc; clear all; close all;
+
+% Method 1
+% x_vec = -2:0.001:2;
+% unit_step_vec = []
+% for ind = 1:length(x_vec)
+%     x = x_vec(ind);
+%     if x >= 0 
+%         unit_step = 1;
+%     else
+%         unit_step = 0;
+%     end
+%     unit_step_vec = [unit_step_vec unit_step] ;
+% end
+% figure
+% plot(x_vec, unit_step_vec,'x-b')
+
+% Method 2
+% x_vec = -2:0.001:2;
+% unit_step_vec = (x_vec >= 0);
+% figure
+% plot(x_vec, unit_step_vec,'x-b')
+
+% Method 3
+% unit_step = @(x) (x >=0 );
+% fplot(unit_step)
+
+% For indicator functions
+x_vec = -2:0.001:6;
+a = 2; b =4;
+indicator_vec = (x_vec >= a)&(x_vec < b);
+figure
+plot(x_vec, indicator_vec,'x-b')

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture5_Example Codes/lec5_ex2.m

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+% Use indicator functions to represent a general function
+clc; clear all; close all;
+
+% Figure 1
+x_vec = -2:0.001:4;
+% fx_vec = 2*x_vec.*((x_vec >= 0)&(x_vec < 0.5)) + 1*((x_vec >= 0.5)&(x_vec < 1.5))+ (4-2*x_vec).*((x_vec >= 1.5)&(x_vec < 2));
+fx_vec = 2*x_vec.*indi_func(x_vec,0,0.5)+indi_func(x_vec,0.5,1.5)+(4-2*x_vec).*indi_func(x_vec,1.5,2);
+
+% Figure 2 
+fx_scaled = 2*fx_vec;
+
+figure
+subplot(1,2,1)    % For Figure 1
+plot(x_vec, fx_vec,'-b','linewidth',2)
+grid on
+xlabel('x'); ylabel('f(x)')
+title('f(x) versus x')
+ylim([0 2])
+subplot(1,2,2)    % For Figure 2
+plot(x_vec, fx_scaled,'-r','linewidth',2)
+grid on
+xlabel('x'); ylabel('2*f(x)')
+title('2*f(x) versus x')

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex1.m

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+clear all; close all; clc;
+
+% Slide 7 in Lecture 6.
+% k1 = [1; 0; -2];
+% k2 = [0; 3; 1];
+% x = [];
+% for k = [k1,k2]
+%     x = [x, 3.0 + 0.1*k];
+% end
+
+% Slide 8 in Lecture 6
+for k = [3, 7, 10]
+    x(k) = 3 + 0.1*k;
+    disp(x);
+end

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex2.m

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+% Some methods to compute S = 1 + 1/2^2 + 1/3^2 +...
+clear all; close all; clc;
+
+% Cumsum function
+N=1:1000; S1 = cumsum(1./(N.^2)); S1(1000) 
+
+% While-Loops
+N=1000; k=1; S2=0;
+while k<=N;
+    S2=S2+1/k^2; k=k+1;
+end
+disp(S2)
+
+% For-Loops
+n=1000; S3 = 0;
+for k=1:n
+    S3=S3+1/k^2;
+end
+disp(S3)

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex3.m

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+% Generate a random matrix and compute the squared norm of the matrix
+% x = [x11 x12; x21 x22] and ||x||^2 = x11^2 + x12^2 + x21^2 + x22^2
+
+clear all; close all; clc; 
+
+n = input('Number of row is ')
+m = input('Number of column is ')
+% Generate a random matrix n x m
+A = randn(n,m);
+
+% Compute the squared norm of the matrix
+% Double-Loop
+norm1 = 0;
+for i=1:n
+    for j=1:m
+        norm1 = norm1 + abs(A(i,j))^2;
+    end
+end
+norm1
+
+% Matrix-based Method
+norm2 = sum(sum(abs(A).^2))
+

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex4.m

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+% Compute infinte sum S(n) = 1/1^2 + 1/2^2 +... + 1/n^2 when n goes to infinity 
+% with the relative error |S(n) - S(n-1)|/|S(n-1)| < 10^(-10)
+% Notice that S(n) - S(n-1) = 1/n^2
+
+clear all; close all; clc;
+S = 0; n = 1;
+while n > 0
+    error = (1/n^2)/S;
+    if error < 10^(-10)
+        break;
+    else
+        S = S + 1/n^2; 
+        n = n + 1;  
+    end    
+end
+S

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex5.m

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+% S(n) = sum of (-1/3)^k/(2k+1) for k=0,1,2,..,n. 
+% with the relative error |S(n) - S(n-1)|/|S(n-1)| < 10^(-10)
+% Notice that S(n) - S(n-1) = (-1/3)^n/(2n+1)
+% Plot S(n) versus n
+
+clear all; close all; clc;
+S_vec = [];
+S = 0; k = 0;
+while k > -1
+    error = abs((-1/3)^k/(2*k+1))/abs(S);
+    if error < 10^(-5)
+        break;
+    else
+        S = S + (-1/3)^k/(2*k+1); 
+        S_vec = [S_vec S];
+        k = k + 1;          
+    end    
+end
+n_vec = 0:length(S_vec)-1;
+plot(n_vec,S_vec)
+xlabel('n'); ylabel('S(n)')

Introduction to Computer for Engineers_Minh/2021_Summer_Example Codes/Lecture6_Example Codes/Lec6_Ex6.m

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+% This code is to compute the square-root algorithm
+% The requirement is to get all values of sequences 
+% such as the error |x(n)-x(n-1)|/|x(n-1)| < 10^(-6) 
+% Hint: get x_vec = [x(1),....,x(n)] and use while-loop
+
+clear all; close all; clc;
+a = 20;
+n = 2; x_vec = [20]; 
+while n > 0
+    x_vec = [x_vec sub_func_Ex6(n,a)];
+    error = abs(sub_func_Ex6(n,a) - sub_func_Ex6(n-1,a))/abs(sub_func_Ex6(n-1,a));
+    if error < 10^(-10)
+        break;
+    else
+        n = n + 1;
+    end
+end
+plot(1:length(x_vec), x_vec)