clear all;


%% Create a gaussian

% Params:
freq=logspace;                  % frequency of the sine wave (Hz)
sampRate=1000;            % sampling rate

% Centered time vector
time = -2:1/sampRate:2;
% make a Gaussian
c = logspace;
s = c/(2*pi*freq);
gaussian_win = exp(-time.^2./(2*s^2));

for 1:length(vetor)

    wavelet = sinewave .* gaussian_win;
end


figure, clf ; set(gcf, 'color','w', 'WindowState', 'maximize');
plot( time,gaussian_win ,LineWidth=5,Color='#b31084');
box off;grid on
ax = gca; % Get current axes handle
ax.LineWidth = 4;
ax.FontSize = 20;
ax.GridLineWidth = 1;




%% Create a sine wave

% make a sine wave
sinewave =  exp( 1i*2*pi*freq*time);


figure, clf ; set(gcf, 'color','w', 'WindowState', 'maximize');
plot(time, sinewave, 'b-',LineWidth=7,Color='#b31084');
box off
ax = gca; % Get current axes handle
ax.LineWidth = 4;
ax.FontSize = 20;


%% create a morlet wavelet

wavelet = sinewave .* gaussian_win;

figure, clf ; set(gcf, 'color','w', 'WindowState', 'maximize');
plot( time,wavelet ,LineWidth=5,Color='#b31084');
box off;grid on
ax = gca; % Get current axes handle
ax.LineWidth = 4;
ax.FontSize = 20;

%% FFT
numPoints=sampRate*2;     
all_size = round(size(wavelet,2)/4);
long_nfft = numPoints;
hann_all = .5 - cos(2*pi*linspace(0,1,size(wavelet,2)))./2;

[cmx_welch,welch_hz] = pwelch(wavelet,hann_all,all_size,long_nfft,sampRate);
[bsd_welch,welch_hz] = pwelch(sinewave,hann_all,all_size,long_nfft,sampRate);
 
  
figure(1), clf
set(gcf, 'color','w', 'Position', get(0, 'Screensize'))
subplot(1,1,1)
    plot(welch_hz,10*log10(cmx_welch(1:length(welch_hz))),'linew',2),hold on
    plot(welch_hz,10*log10(bsd_welch(1:length(welch_hz))),'linew',2)
    
        xlabel('Frequency (Hz)'), ylabel('Power(dB)')
        title ('Wavelet vs. Sine ')
        set(gca,'xlim',[1 30])
        legend('wavelet','sine wave')
        axis square
        box off
        grid on