Øving 6, Digsig

%% Øving 6, Digital signalbehandling, Henning Schei
%
%% Oppgave 1

% a)
Nx= 28;
f = linspace(0,1,10000);
X = (1 - (power(0.9*exp(1j*2*pi*f), Nx)))./(1- (0.9*exp(1j*2*pi*f)));
plot (f, abs(X));
title 'Magnutide response'
xlabel 'Frequency'

% b)
n = 0:Nx-1;
x = power(0.9,n);
N = [Nx/4, Nx/2, Nx, 2*Nx ];

X1 = fft(x,N(1)); X2 = fft(x,N(2));
X3 = fft(x,N(3)); X4 = fft(x, N(4));




% d)
figure
subplot(2,2,1)
hold on
plot(f,abs(X));
freq= linspace(0,1, length(X1));
stem(freq,abs(X1));
title 'Magnitude DTFT and DFT with length = 7'

subplot(2,2,2)
hold on
plot(f,abs(X));
freq= linspace(0,1, length(X2));
stem(freq,abs(X2));
title 'Magnitude DTFT and DFT with length = 14'

subplot(2,2,3)
plot(f,abs(X));
hold on
freq= linspace(0,1, length(X3));
stem(freq,abs(X3));
title 'Magnitude DTFT and DFT with length = 28'

subplot(2,2,4)
plot(f,abs(X));
hold on
freq= linspace(0,1, length(X4));
stem(freq,abs(X4));
title 'Magnitude DTFT and DFT with length = 56'



%% Oppgave 2
% a)
clear all
Nh = 9;
Nx = 28;
n  = 0:Nx-1;
h  = ones(1,Nh);
x  = power(0.9,n);
y  = conv(x,h);
Ny = 0:(length(x) + length(h) -2);
figure
stem(Ny,y)
title 'Time domain convolution of x[n] and h[n]'
xlabel 'n'
ylabel 'y[n]'

% b)
% Computing y[n] via the frecuency domain
N  = (1/2)*(Nx + Nh -1);
X  = fft(x, N); H = fft(h, N);
Y  = X .* H;
n  = 0:N-1;
y  = ifft(Y, N);
figure
stem(n,y)
Ny = Nx + Nh -1;
% Plotting with different values of $N_y$;
N_set = [Ny/4, Ny/2, Ny, 2*Ny];
for i=1:length(N_set)
    DFT_IFT(x,h, N_set(i));
end


% DFT-lengths must at lest be equal to the length of Ny to avoid time
% domain alaiasing, as the plots show.


clear all
%% Oppgave 3
% b)

f1 = 7/40; f2 = 9/40;
n  = 0:100-1;
x  = sin(2*pi*f1*n) + sin(2*pi*f2*n);
N  = 1024;
X  = fft(x,N);
f  = linspace(0,0.5, length(X));
plot(f,abs(X));

% Repeating with different segment lengths of n
n_ = [1000, 30, 10];
figure
for i=1:3
    n  = 0:n_(i) -1;
    x  = sin(2*pi*f1*n) + sin(2*pi*f2*n);
    N  = 1024;
    X  = fft(x,N);
    f  = linspace(0,0.5, length(X));
    subplot(2,2,i)
    plot(f,abs(X));
    xlabel 'f'
    title (['DFT of x[n] with length n = ' num2str(n_(i))])

end
% c) Repeating b) with segment length N = 100 and different DFT lengths
DFT_length=[256, 128];
n= 0:100-1;
N = DFT_length(1);
x  = sin(2*pi*f1*n) + sin(2*pi*f2*n);
X  = fft(x,N);
f  = linspace(0,0.5, length(X));
figure
subplot(2,1,1)
plot(f,abs(X));
xlabel 'f'
title 'DFT- length = 256'
N = DFT_length(2);
x  = sin(2*pi*f1*n) + sin(2*pi*f2*n);
X  = fft(x,N);
f  = linspace(0,0.5, length(X));
subplot(2,1,2)
plot(f,abs(X))
xlabel 'f'
title 'DFT- length = 128'