fname = 'C:\Users\Joe\Google Drive\MAT598 Fourier\HW4'; %desktop
%fname = '/Users/joesadow/Google Drive/MAT598 Fourier/HW4'; %mac
%% Initiate and compute FFT
warning off; 
f = @(t) exp(-t.^2./10).*(sin(2*t) + 2*cos(4*t) + 0.4.*sin(t).*sin(50.*t));
t = -7:0.1:7; 
j = 1:256;
freqax = 2*pi.*j./256;
y = f(2*pi.*j./256); %discrete version of signal 
yhat = fft(y); %DFT 
%% Filter
M = [6 10 15 30]; %various m values
P = []; %percent of coeff filtered out
for l = 1:numel(M)
    m = M(l); 
    filterout = m:255-m; 
    yhatf = yhat; yhatf(filterout) = 0; 
    f_fil = ifft(yhatf);
    perct = numel(yhatf(filterout))/numel(yhat);
    P = [P perct]; 
   
     
    fig = figure; %generate and save filtered signal plots
    plot(j,y,'k',j,f_fil,'r')
    str = strcat({'f with filtered f (m = '}, num2str(m),')');
    title(str);
    legend('Original Signal','Filtered Signal')
    xlabel('t')
    ylabel('f(t)')
    str2 = strcat(num2str(l));
    saveas(fig, fullfile(fname, str2), 'epsc');   
end 
    fig = figure; %generate and save filtered DFT plots
    plot(freqax,abs(yhat),'*k',freqax,abs(yhatf),'*r')
    str = strcat({'DFT of f with filtered DFT (m = '}, num2str(m),')');
    title(str);
    legend('Original DFT','Filtered DFT')
    xlabel('frequency')
    ylabel('fft')
    str2 = strcat(num2str(5));
    saveas(fig, fullfile(fname, str2), 'epsc');
    
T = table(M',P','VariableNames',{'m','PercentCoeff'});
disp(T); 
%% Compress 
tol = [.5 1 10 20]; %various tolerances
P = []; %percent of coeff filtered out
Err = []; %relative error in L2 sense
for l = 1:numel(tol)
    epsi = tol(l); 
    yhatc = yhat; 
    yhatc(find(yhat < epsi))  = 0;  
    f_c = ifft(yhatc);
    perct = numel(yhatc(find(yhat < epsi)))/numel(yhatc);
    P = [P perct]; 
    l2err = norm(yhat - yhatc,2)/norm(yhat,2); 
    Err = [Err l2err]; 
     
    fig = figure; %generate and save compressed signal plots
    plot(j,y,'k',j,f_c,'r')
    str = strcat({'f with compressed f with %'},num2str(100*perct),... 
        ' coefficients taken out');
    title(str);
    legend('Original Signal','Compressed Signal')
    xlabel('t')
    ylabel('f(t)')
    str2 = strcat(num2str(l+5));
    saveas(fig, fullfile(fname, str2), 'epsc');   
end 
T = table(tol',P',Err','VariableNames',{'Tolerance','PercentCoeff', 'L2CompressionError'});
disp(T);