%%   median filtering

>> j = imread('eight.jpg');
>> subplot(1,3,1);
>> imshow(j)
>> k = imnoise(j , 'salt & pepper');
>> subplot(1,3,2);
>> imshow(k);
>> r = rgb2gray(k);
>> c = medfilt2(r, [3 3]);
>> subplot(1,3,3);
>> imshow(r)

%%  mean convolution

>> j = imread('cameraman.jpg');
>> imshow(j);
>> h = [1 1 1;1 1 1;1 1 1] / 9 ;
>> c = imfilter(j,h);
>> imshow(c)

%%  connected component
 
I = imread('grains2.jpg');
>> imshow(I)
>> j = rgb2gray(I);
>> j2 = ThresholdingFirst(j);
>> cc = bwconncomp(j,8);
>> n = cc.NumObjects;

%%  edge detection (sobel)

>> j = imread('cameraman.jpg');
>> r = rgb2gray(j);
>> h = [1 0 -1;2 0 -2;1 0 -1]
>> c = imfilter(r,h);
>> imshow(c)
>> 

%%   edge detection (canny) 

BW = edge(r , 'canny');
imshow(BW)

%% fourier series of a square wave

syms n t
>> w0 = pi;
>> T0 = 2;
>> n = 1:5;
>> a0 = (1/T0) * int(1,t,0,1)
 an = (2/T0) * int(cos(n*w0*t),t,0,1)
 bn = (2/T0) * int(sin(n*w0*t),t,0,1)

%%  fourier transformation

 Fs = 1000; %% sampling frequency
>> Ts = 1/Fs;  %% sampling period
>> dt = 0:Ts:2-Ts ; % signal duration
>>  
>> f1 = 10;
>> f2 = 30;
>> f3 = 70;
>> 
>> y1 = 10 * sin(2*pi*f1*dt);
>> y2 = 10 * sin(2*pi*f2*dt);
>> y3 = 10 * sin(2*pi*f3*dt);
>> 
>> y = y1+y2+y3 ;
>> 
>> subplot(4,1,1) ; plot(dt,y1,'r');
>> subplot(4,1,2) ; plot(dt,y2,'r');
>> subplot(4,1,3) ; plot(dt,y3,'r');
>> subplot(4,1,4) ; plot(dt,y,'r');