Lab8

%------------------------------------------Task1
clc;
clear all;

x = [1,2];
N = 2;

X = zeros(1,2);

X(1) = x(1) + x(2);
X(2) = x(1) - x(2);

y = fft(x);

figure
plot(x);
figure
plot(y);


%-------------------------------------------Task2
clc;
clear all;
close all;
x = [1,2,3,4];
N = length(x);
k = [0,1,2,3];
Wkn = zeros(1,length(k));
for i = 1 : length(x)
    Wkn(i) = exp(-2*1i*pi*k(i)/N);
end
X = zeros(1,4);
V11 =  x(1) + Wkn(1)*x(3);
V12 =  x(1) - Wkn(1)*x(3);
V13 =  x(2) + Wkn(1)*x(4);
V14 =  x(2) - Wkn(1)*x(4);
X(1) =  V11 + Wkn(1)*V13;
X(2) = V12 + Wkn(2)*V14;
X(3) =  V11 - V13;
X(4) =  V14*Wkn(2) + V12;
Y = fft(x);
subplot(2,1,1)
stem(X);
title('My FFT');
subplot(2,1,2);
stem(Y);
title("In-built FFT");

%---------------------------------------------Task3
clc;
clear all;
close all;
x = [1, 2, 3, 4];
X=x;
N = length(x);
Half = 1;
V = log2(N);
butterfly_no = N/2;
x = [x, zeros(1, 2^V -N)];
x = bitrevorder(x);
for level = 1: V
for index = 0: 2^level:N-1
for n = 0 : (Half -1)
position = n + index + 1;
power = (2^(V-level))*n;
w = exp(-2*1i* pi * power /N);
a = x(position) + x(position + Half).*w;
b = x(position) - x(position + Half).*w;
x(position) = a;
x(position + Half) = b;
end
end
Half = Half * 2;
end
subplot(3, 1, 1)
stem(X);
title('Input Signal');
subplot(3,1, 2)
stem(abs(x));
title('myFFT');
subplot(3,1,3)
Y = fft(X)
stem(abs(Y));
title('In-built FFT');

%---------------------------------------------Task4
clc;
clear all;
close all;
n=[2 4 8 16 32 64 128];
N=length(n);
speed=zeros(1,N);
for i=1:N
    speed(i)=(n(i)*n(i))/((n(i)/2)*log2(n(i)));
end
stem(n,speed);
ylabel('Speed-factor');
xlabel('n');
title('Speed-factor V/s N - 21ucc030');