I understand that you're looking to illustrate wavelets between two lines that pass through the origin. The goal is to determine the lengths of the long and short wavelets and plot their shifted versions. Below is a sample script that demonstrates how to draw a Morlet wavelet between lines with slopes of 5 and 1, and how to shift these wavelets to y = 4 and y = 6.
close all;
% Define the slopes of the two lines
slope1 = 5;
slope2 = 1;
% Define a range for the x-values in the first quadrant (positive values)
x = 0:0.01:10;
% Calculate the corresponding y-values for each line
y1 = slope1 * x;
y2 = slope2 * x;
% Calculate the x-values where the lines intersect y = 4 and y = 6
xs1 = 4 / slope1;
xs2 = 4 / slope2;
WaveletLengthShort=xs2-xs1;
xl1 = 6 / slope1;
xl2 = 6 / slope2;
WaveletLengthLong=xl2-xl1;
w0 = 2;
t=-3:0.01:9 ;
t_long = -WaveletLengthLong*0.5:0.01:WaveletLengthLong*0.5;
sigma1 = 0.75; % Standard deviation of the Gaussian window
% Morlet Wavelet (Real part only)
morlet_wavelet = (pi^(-0.25)) * exp(2i * pi * w0 * t_long) .* exp(-t_long.^2 / (2 * sigma1^2));
t_shifted1 = t_long +WaveletLengthLong*0.5+xl1;
y_shifted1 = 6 * ones(size(t));
indices1 = (t >= min(t_shifted1) & t <= max(t_shifted1) );
y_shifted1(indices1) = y_shifted1(indices1) + (morlet_wavelet);
% Create a shorter second wavelet
t_short = -WaveletLengthShort*0.5:0.01:WaveletLengthShort*0.5; % Shorter time vector
sigma2=0.5;
morlet_wavelet_short = 0.8*(pi^(-0.25)) * exp(2i * pi * w0 * t_short) .* exp(-t_short.^2 / (2 * sigma2^2));
% Shift the second wavelet to the right by 1 unit and plot at y = 1
t_shifted2 = t_short + WaveletLengthShort*0.5+xs1;
y_shifted2 = 4 * ones(size(t));
% Find indices in the original time vector that match the shifted short wavelet
indices2 = (t >= min(t_shifted2) & t <= max(t_shifted2));
y_shifted2(indices2) = y_shifted2(indices2) + (morlet_wavelet_short);
figure;
plot(x, y1, 'k');
hold on;
plot(x, y2, 'k');
plot(t, real(y_shifted1), 'b');
plot(t, real(y_shifted2), 'r');
hold off;
ylim([0 8])
xlim([0 8])
Adjust any parameters as needed to fit your specific requirements.
