clear all; close all

%NoteVec = [  27.500   29.135   30.863   32.703   34.648   36.708   38.891   41.203   43.654   46.249   48.999   51.913...
%             55.000   58.270   61.735   65.406   69.269   73.416   77.782   82.407   87.307   92.499   97.999  103.830...
%            110.000  116.540  123.470  130.810  138.590  146.830  155.560  164.810  174.610  185.000  196.000  207.650...
%            220.000  233.080  246.950  261.630  277.180  293.660  311.130  329.630  349.230  369.990  392.000  415.300...
%            440.000  466.160  493.880  523.550  554.370  587.330  622.260  659.260  698.460  739.990  783.990  830.610...
%            880.000  932.330  987.770 1046.500 1108.700 1174.700 1244.500 1318.500 1396.900 1480.000 1568.000 1661.200...
%           1760.000 1864.700 1975.500 2093.000 2217.500 2349.300 2489.000 2637.000 2793.000 2960.000 3136.000 3322.400...
%           3520.000 3729.300 3951.100 4186.000...
%          ];
      
load handel 
v = y'/2; 
%plot((1:length(v))/Fs,v); 
%xlabel('Time [sec]'); 
%ylabel('Amplitude'); 
%title('Signal of Interest, v(n)');
n = length(v);
L = n./Fs;
t2=linspace(0,L,n+1); 
t=t2(1:n); 
k=(2*pi/L)*[0:n/2-1 -n/2:-1]; 
ks=fftshift(k);
width = [4 2 1 1/2 1/4 1/8 1/16 1/32];


tstep = 1.25;
tslide = 1/Fs:tstep:n/Fs;

Sgt_spec1 = zeros(4,8,length(tslide),16384);

for k = 1:length(width)
    for j = 1:length(tslide)
        g_gauss = exp(-(t-tslide(j)).^2./(2.*width(k).^2));  
        g_rect = rectpuls(t-tslide(j),2.*width(k));
        g_mxhat = (1-((t-tslide(j)).^2)./(width(k).^2)).*exp(-(t-tslide(j)).^2./(2.*width(k).^2)); 
        g_sinc = 2.*sinc(2./width(k).*(t-tslide(j))) - sinc(1./width(k).*(t-tslide(j)));
    
        Sg_gauss = g_gauss.*v;
        Sg_rect = g_rect.*v;
        Sg_mxhat = g_mxhat.*v;
        Sg_sinc = g_sinc.*v;
    
        Sgt_gauss = abs(fftshift(fft(Sg_gauss)));
        Sgt_rect = abs(fftshift(fft(Sg_rect)));
        Sgt_mxhat = abs(fftshift(fft(Sg_mxhat)));
        Sgt_sinc = abs(fftshift(fft(Sg_sinc)));
        
        Sgt_spec1(1,k,j,:) = Sgt_gauss((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec1(2,k,j,:) = Sgt_rect((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec1(3,k,j,:) = Sgt_mxhat((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec1(4,k,j,:) = Sgt_sinc((floor(end/2)+1):(floor(end/2)+16384));
        [k j]
    end
end

tstep = .125;
tslide = 1/Fs:tstep:n/Fs;

Sgt_spec2 = zeros(4,8,length(tslide),16384);

for k = 1:length(width)
    for j = 1:length(tslide)
        g_gauss = exp(-(t-tslide(j)).^2./(2.*width(k).^2));  
        g_rect = rectpuls(t-tslide(j),width(k));
        g_mxhat = (1-((t-tslide(j)).^2)./(width(k).^2)).*exp(-(t-tslide(j)).^2./(2.*width(k).^2)); 
        g_sinc = 2.*sinc(2./width(k).*(t-tslide(j))) - sinc(1./width(k).*(t-tslide(j)));
    
        Sg_gauss = g_gauss.*v;
        Sg_rect = g_rect.*v;
        Sg_mxhat = g_mxhat.*v;
        Sg_sinc = g_sinc.*v;
    
        Sgt_gauss = abs(fftshift(fft(Sg_gauss)));
        Sgt_rect = abs(fftshift(fft(Sg_rect)));
        Sgt_mxhat = abs(fftshift(fft(Sg_mxhat)));
        Sgt_sinc = abs(fftshift(fft(Sg_sinc)));
        
        Sgt_spec2(1,k,j,:) = Sgt_gauss((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec2(2,k,j,:) = Sgt_rect((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec2(3,k,j,:) = Sgt_mxhat((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec2(4,k,j,:) = Sgt_sinc((floor(end/2)+1):(floor(end/2)+16384));
        [k j]
    end
end

tstep = .0125;
tslide = 1/Fs:tstep:n/Fs;

Sgt_spec3 = zeros(4,8,length(tslide),16384);

for k = 1:length(width)
    for j = 1:length(tslide)
        g_gauss = exp(-(t-tslide(j)).^2./(2.*width(k).^2));  
        g_rect = rectpuls(t-tslide(j),width(k));
        g_mxhat = (1-((t-tslide(j)).^2)./(width(k).^2)).*exp(-(t-tslide(j)).^2./(2.*width(k).^2)); 
        g_sinc = 2.*sinc(2./width(k).*(t-tslide(j))) - sinc(1./width(k).*(t-tslide(j)));
    
        Sg_gauss = g_gauss.*v;
        Sg_rect = g_rect.*v;
        Sg_mxhat = g_mxhat.*v;
        Sg_sinc = g_sinc.*v;
    
        Sgt_gauss = abs(fftshift(fft(Sg_gauss)));
        Sgt_rect = abs(fftshift(fft(Sg_rect)));
        Sgt_mxhat = abs(fftshift(fft(Sg_mxhat)));
        Sgt_sinc = abs(fftshift(fft(Sg_sinc)));
        
        Sgt_spec3(1,k,j,:) = Sgt_gauss((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec3(2,k,j,:) = Sgt_rect((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec3(3,k,j,:) = Sgt_mxhat((floor(end/2)+1):(floor(end/2)+16384));
        Sgt_spec3(4,k,j,:) = Sgt_sinc((floor(end/2)+1):(floor(end/2)+16384));
        [k j]
    end
end

tstep1 = 1.25;
tslide1 = 1/Fs:tstep1:n/Fs;

tstep2 = 0.125;
tslide2 = 1/Fs:tstep2:n/Fs;

tstep3 = .0125;
tslide3 = 1/Fs:tstep3:n/Fs;

save('./AMath582hw3p1.mat','ts*','ks','Sgt_spec*','-v7.3')