update LAB 4

% 4.2(a)

% 4.2(b)

tau = 0.01

T = 10

N = T/tau

t = [0:tau:T-tau]

y = exp(-2 * abs(t-5))

%4.2(c)

Y = fftshift(tau*fft(y))

%4.2(d)

w = -(pi/tau)+(0:N-1)*(2*pi/(N*tau))

%4.2(e)

X = exp(j*5*w).*Y

%4.2(f)

magnitudeX_app = abs(X)

phaseX_app = angle(X)

x = exp(-2 * abs(t))

X2 = fftshift(tau * fft(x))

magnitudeX = abs(X2)

phaseX = angle(X2)

% plot(t, x, 'g');

% hold on;

% plot(t, y, 'b');

figure;

subplot(2, 1, 1)

hold on

plot(w, magnitudeX_app , 'g')

plot(w, magnitudeX, 'b')

legend('|X| by approximation', '|X|', 'Location', 'northeast');

title('magnitude of X and approximation of X');

subplot(2, 1, 2)

hold on

plot(w, phaseX_app, 'g')

plot(w, phaseX, 'b')

legend('|X| by approximation', '|X|', 'Location', 'northeast');

title('phase of X and approximation of X');

saveas(gcf, "plots/P4_2_f_out1.png")

close

%4.2(g)

magnitudeY = abs(Y)

phaseY = angle(Y)

figure;

subplot(2, 1, 1)

hold on

plot(w, magnitudeY , 'g')

plot(w, magnitudeX, 'b')

legend('Y', 'X', 'Location', 'northeast');

title('magnitude of X and Y');

subplot(2, 1, 2)

hold on

plot(w, phaseY, 'g')

plot(w, phaseX, 'b')

legend('Y', 'X', 'Location', 'northeast');

title('phase of X and Y');

saveas(gcf, "plots/P4_2_f_out2.png")

close

% 4.2(a)

% 4.2(b)

tau = 0.01

T = 10

N = T/tau

t = [0:tau:T-tau]

y = exp(-2 * abs(t-5))

%4.2(c)

Y = fftshift(tau*fft(y))

%4.2(d)

w = -(pi/tau)+(0:N-1)*(2*pi/(N*tau))

%4.2(e)

X = exp(j*5*w).*Y

%4.2(f)

magnitudeX_app = abs(X)

phaseX_app = angle(X)

x = exp(-2 * abs(t))

X2 = fftshift(tau * fft(x))

magnitudeX = abs(X2)

phaseX = angle(X2)

% plot(t, x, 'g');

% hold on;

% plot(t, y, 'b');

figure;

subplot(2, 1, 1)

hold on

plot(w, magnitudeX_app , 'g')

plot(w, magnitudeX, 'b')

legend('|X| by approximation', '|X|', 'Location', 'northeast');

title('magnitude of X and approximation of X');

subplot(2, 1, 2)

hold on

plot(w, phaseX_app, 'g')

plot(w, phaseX, 'b')

legend('|X| by approximation', '|X|', 'Location', 'northeast');

title('phase of X and approximation of X');

saveas(gcf, "plots/P4_2_f_out1.png")

close

%4.2(g)

magnitudeY = abs(Y)

phaseY = angle(Y)

figure;

subplot(2, 1, 1)

hold on

plot(w, magnitudeY , 'g')

plot(w, magnitudeX, 'b')

legend('Y', 'X', 'Location', 'northeast');

title('magnitude of X and Y');

subplot(2, 1, 2)

hold on

plot(w, phaseY, 'g')

plot(w, phaseX, 'b')

legend('Y', 'X', 'Location', 'northeast');

title('phase of X and Y');

saveas(gcf, "plots/P4_2_f_out2.png")

close