% *******************************************************************
%                          DSP Project #4
% *******************************************************************

FS = 2000; startp = 0; endp = 10;
N = startp:1/FS:endp;

% ========================
%            A
% ========================

xA = unitstep(0, startp, endp) - unitstep(6, startp, endp);
yA = (1/FS) * fftshift(fft(xA));
fA = linspace(-FS/2, FS/2, length(yA));
figure;
subplot(1,2,1);
plot(fA, abs(yA));
subplot(1,2,2);
plot(fA, angle(yA));

% ========================
%            B
% ========================

xB = 2.^N .* linspace(0, 0, length(N));
yB = (1/FS) * fftshift(fft(xB));
fB = linspace(-FS/2, FS/2, length(yB));
figure;
subplot(1,2,1);
plot(fB, abs(yB));
subplot(1,2,2);
plot(fB, angle(yB));
% reflected unitstep from 0 -> 10 will be 0
% So akid kolo 7ikon zero -_-

% ========================
%            C
% ========================

xC = (1/4).^N .* linspace(1, 1, length(N));
yC = (1/FS) * fftshift(fft(xC));
fC = linspace(-FS/2, FS/2, length(yC));
figure;
subplot(1,2,1);
plot(fC, abs(yC));
subplot(1,2,2);
plot(fC, angle(yC));
% Unit step start before the start point
% So from -4 or (0 -> startpoint) till the end = 1

% ========================
%            D
% ========================

xD11 = (0.25 .^ N);
xD12 = sin(2 * pi * 0.25 * N);
xD1  = xD11 .* xD12;
xD2  = linspace(1, 1, length(N));
xD   = xD1 .* xD2;
yD   = (1/FS) * fftshift(fft(xD));
fD   = linspace(-FS/2, FS/2, length(yD));
figure;
subplot(1,2,1);
plot(fD, abs(yD));
subplot(1,2,2);
plot(fD, angle(yD));

% ========================
%            E
% ========================

xE11 = (0.5 .^ N);
xE12 = sin(2 * pi * 0.25 * N);
xE  = xE11 .* xE12;
yE   = (1/FS) * fftshift(fft(xE));
fE   = linspace(-FS/2, FS/2, length(yE));
figure;
subplot(1,2,1);
plot(fE, abs(yE));
subplot(1,2,2);
plot(fE, angle(yE));

% ========================
%            F
% ========================

startp = -4; endp = 4;
N  = startp:1/FS:endp;
xF = 2-(0.5 .* N);
yF = (1/FS) * fftshift(fft(xF));
fF = linspace(-FS/2, FS/2, length(yF));
figure;
subplot(1,2,1);
plot(fF, abs(yF));
subplot(1,2,2);
plot(fF, angle(yF));

% ========================
%            G
% ========================

startp = -2; endp = 2;
FS = 1;
N  = startp:1/FS:endp;
xG = [-2 -1 0 1 2];
yG = fftshift(fft(xG));
fG = linspace(-1/2, 1/2, length(yG));
figure;
subplot(1,2,1);
plot(fG, abs(yG));
subplot(1,2,2);
plot(fG, angle(yG));