clc,clear; % FT
Ts = 1/50;
t = 0:Ts:10-Ts;
x = (sin(2*pi*15*t) + sin(2*pi*20*t));
plot(t,x)
xlabel('Time (seconds)')
ylabel('Amplitude');
clc,clear;
Ts = 1/50;
t = 0:Ts:10-Ts;
x = (sin(2*pi*15*t) + sin(2*pi*20*t));
y = fft(x);
fs = 1/Ts;
f = (0:length(y)-1)*fs/length(y);
plot(f,abs(y));
xlabel('Frequency (Hz)');
ylabel('Magnitude');
title('Magnitude');
clc,clear;
Ts = 1/50;
t = 0:Ts:10-Ts;
x = (sin(2*pi*15*t) + sin(2*pi*20*t));
y = fft(x);
fs = 1/Ts;
n = length(x);
fshift = (-n/2:n/2-1)*(fs/n);
yshift = fftshift(y);
plot(fshift,abs(yshift));
xlabel('Frequency (Hz)');
ylabel('Magnitude');
clc,clear;
Ts = 1/50;
t = 0:Ts:10-Ts;
x = (sin(2*pi*15*t) + sin(2*pi*20*t));
fs = 1/Ts;
n = length(x);
fshift = (-n/2:n/2-1)*(fs/n);
rng('default')
xnoise = x + 2.5*randn(size(t));
ynoise = fft(xnoise);
ynoiseshift = fftshift(ynoise);
power = abs(ynoiseshift).^2/n;
plot(fshift,power)
title('Power');
xlabel('Frequency (Hz)');
ylabel('Power');
clc,clear;
fs = 100;
t = 0:1/fs:1-1/fs;
x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t);
y = fft(x);
z = fftshift(y);
ly = length(y);
f = (-ly/2:ly/2-1)/ly*fs;
stem(f,abs(z));
xlabel('Frequency (Hz)');
ylabel('|y|');
grid
clc,clear;
fs = 100;
t = 0:1/fs:1-1/fs;
x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t);
y = fft(x);
z = fftshift(y);
ly = length(y);
f = (-ly/2:ly/2-1)/ly*fs;
tol = 1e-6;
z(abs(z) < tol) = 0;
theta = angle(z);
stem(f,theta/pi)
xlabel('Frequency (Hz)')
ylabel('Phase / \pi')
grid
clc,clear; % DFT
t = 0:1/100:10-1/100; % Time vector
x = sin(2*pi*15*t) + sin(2*pi*40*t); % Signal
y = fft(x); % Compute DFT of x
m = abs(y); % Magnitude
y(m<1e-6) = 0;
p = unwrap(angle(y)); % Phase
f = (0:length(y)-1)*100/length(y); % Frequency vector
subplot(2,1,1)
plot(f,m)
title('Magnitude')
ax = gca;
ax.XTick = [15 40 60 85];
subplot(2,1,2)
plot(f,p*180/pi)
title('Phase')
ax = gca;
ax.XTick = [15 40 60 85];
clc,clear;
n = 512;
y = fft(x,n);
m = abs(y);
p = unwrap(angle(y));
f = (0:length(y)-1)*100/length(y);
subplot(2,1,1)
plot(f,m)
title('Magnitude')
ax = gca;
ax.XTick = [15 40 60 85];
subplot(2,1,2)
plot(f,p*180/pi)
title('Phase')
ax = gca;
ax.XTick = [15 40 60 85];
clc,clear;
t = 0:1/255:1;
x = sin(2*pi*120*t);
y = real(ifft(fft(x)));
figure
plot(t,x-y)
clc,clear; % DCT
clc,clear,close all;
I = imread('cameraman.tif');
I = im2double(I);
T = dctmtx(8);
dct = @(block_struct) T * block_struct.data * T';
B = blockproc(I,[8 8],dct);
mask = [1 1 1 1 0 0 0 0
1 1 1 0 0 0 0 0
1 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0];
B2 = blockproc(B,[8 8],@(block_struct) mask .* block_struct.data);
invdct = @(block_struct) T' * block_struct.data * T;
I2 = blockproc(B2,[8 8],invdct);
imshow([I I2]);
