Hi Amy,
To demonstrate the difference between a Morlet wavelet and a complex Morlet wavelet in MATLAB, we can plot these wavelets to visually inspect their differences. The Morlet wavelet, a commonly used wavelet in continuous wavelet transforms, is essentially a complex sine wave modulated by a Gaussian window. The complex Morlet wavelet, on the other hand, has both real and imaginary components.
Here's how you can plot both the Morlet wavelet and the complex Morlet wavelet in MATLAB:
- Define the Wavelet Parameters: We'll define parameters like the central frequency of the wavelet and the number of points used in the plot.
- Create the Wavelets: We'll use these parameters to create both the Morlet and complex Morlet wavelets.
- Plot the Wavelets: We'll plot the real part, imaginary part, and the magnitude for both wavelets.
Here is an example MATLAB code for this:
% Parameters
w0 = 6; % Central frequency
t = -3:0.01:3; % Time vector
sigma = 1; % Standard deviation of the Gaussian window
% Morlet Wavelet (Real part only)
morlet_wavelet = (pi^(-0.25)) * exp(2i * pi * w0 * t) .* exp(-t.^2 / (2 * sigma^2));
% Complex Morlet Wavelet (Both Real and Imaginary parts)
complex_morlet_wavelet = morlet_wavelet .* exp(-w0^2 / 2);
% Plotting
figure;
% Real part of both wavelets
subplot(3,2,1);
plot(t, real(morlet_wavelet));
title('Real Part of Morlet Wavelet');
subplot(3,2,2);
plot(t, real(complex_morlet_wavelet));
title('Real Part of Complex Morlet Wavelet');
% Imaginary part of both wavelets
subplot(3,2,3);
plot(t, imag(morlet_wavelet));
title('Imaginary Part of Morlet Wavelet');
subplot(3,2,4);
plot(t, imag(complex_morlet_wavelet));
title('Imaginary Part of Complex Morlet Wavelet');
% Magnitude of both wavelets
subplot(3,2,5);
plot(t, abs(morlet_wavelet));
title('Magnitude of Morlet Wavelet');
subplot(3,2,6);
plot(t, abs(complex_morlet_wavelet));
title('Magnitude of Complex Morlet Wavelet');
This code will create a figure with six subplots: the real part, imaginary part, and magnitude of both the Morlet and complex Morlet wavelets. This should help you visually compare the two wavelets.
Remember that the choice of wavelet depends on your specific application and the characteristics of the data you are analyzing. The visual inspection of these wavelets can give you an intuitive understanding of their differences, but the impact of these differences on your continuous wavelet transform results will depend on the nature of your data.
Hope this helps!
