clc; clear all; close all;

%% Experiment 1..... Familiarization with MATLAB

A = 1; w = 0.2*pi; phi = 0;
N = 2*pi/w;
n = 0:0.1:2*N;                     % Two periods, dense sampling

% Sine and Cosine
x_sin = A*sin(w*n + phi);
x_cos = A*cos(w*n + phi);

n_seq = -10:10;
len = length(n_seq);

% ----- Unit Step -----
u = zeros(1,len);
for i = 1:len
    if n_seq(i) >= 0
        u(i) = 1;
    end
end

% ----- Ramp -----
r = zeros(1,len);
for i = 1:len
    if n_seq(i) >= 0
        r(i) = n_seq(i);
    end
end

% ----- Exponential Decrease (a = 0.5) -----
a1 = 0.5;
exp_dec = zeros(1,len);
for i = 1:len
    if n_seq(i) >= 0
        exp_dec(i) = a1^n_seq(i);
    end
end

% ----- Exponential Increase (a = 1.5) -----
a2 = 1.5;
exp_inc = zeros(1,len);
for i = 1:len
    if n_seq(i) >= 0
        exp_inc(i) = a2^n_seq(i);
    end
end

% ----- Unit Sample -----
delta = zeros(1,len);
for i = 1:len
    if n_seq(i) == 0
        delta(i) = 1;
    end
end

figure;

subplot(4,2,1);
stem(n, x_sin, 'filled');
grid on; title('Discrete Sine Wave'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,2);
stem(n, x_cos, 'filled');
grid on; title('Discrete Cosine Wave'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,3);
stem(n_seq, u, 'filled');
grid on; title('Unit Step Sequence'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,4);
stem(n_seq, r, 'filled');
grid on; title('Ramp Sequence'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,5);
stem(n_seq, exp_inc, 'filled');
grid on; title('Exponential Increase (a = 1.5)'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,6);
stem(n_seq, exp_dec, 'filled');
grid on; title('Exponential Decrease (a = 0.5)'); xlabel('n'); ylabel('Amplitude');

subplot(4,2,7);
stem(n_seq, delta, 'filled');
grid on; title('Unit Sample (Impulse)'); xlabel('n'); ylabel('Amplitude');