Try this (untested):
fontSize = 20;
subplot(1, 2, 1);
imshow(yourImage, 'Parent', h1);
title(h1, 'Magnitude Scalogram', 'FontSize', fontSize);
xlabel(h1, 'Time (hours)', 'FontSize', fontSize);
ylabel(h1, 'Period (hours)', 'FontSize', fontSize);
h1 = subplot(1, 2, 1);
imshow(yourImage, 'Parent', h1);
title(h1, 'Magnitude Scalogram', 'FontSize', fontSize);
xlabel('Time (hours)', 'FontSize', fontSize);
ylabel('Period (hours)', 'FontSize', fontSize);
h2 = subplot(1, 2, 2);
semilog(h2, x, y);
title(h2, 'Time Averaged Wavelet Spectrum', 'FontSize', fontSize);
xlabel(h2, 'Density', 'FontSize', fontSize);
ylabel(h2, 'Magnitude', 'FontSize', fontSize);
In general in most functions you can pass in the axis handle to that axes control to have the function operate on only that axes control.
