Obtain the Waviness of Graph

I would like to superimpose the two graphs into one graph by making sure that the peaks of both graphs are at the same point. (Note that each graph has exactly three peaks - highest points) In other words, the superimposed graph must also have only 3 peaks, which are the peaks of graph 1 and also graph 2. During the process, strecthing or shrinking of the graph can be done. The reason of all this is to obtain the graphical demonstration of waviness of second graph. Is there a way to do that?

Attached above is the first graph data and second graph data. The y variable for both graphs is y_graph and x variable for both graphs is x in the mat file.

Below is graph 1.

Below is graph 2.

[Akira Agata]

If possible, could you upload your data as .mat file?

[Ang Xian Jia]

Mat file is uploaded and Question is updated.

Answer 1

[Philippe Lebel]

Does this help you get what you wnat (didn t have the time to finish with the loading ond plotting of data 1)

here is the code (just change max_x_plot_1 for the actual lenght of the plot_1 (didn't load graph1 data))

[max_1,index_1] = max(y_graph);
spacing = floor(length(y_graph)/3);
for i = 1:3
    offsets(i) = (i-1)*spacing;
    [maxes(i), indexes(i)] = max(y_graph((i-1)*spacing + 1:(i*spacing)));
end
indexes = indexes + offsets;
y_graph_trunc = y_graph(indexes(1):indexes(3));
max_x_plot_1 = 2.3*10^4;
ratio = max_x_plot_1 / length(y_graph_trunc);
new_x = 1:ratio:max_x_plot_1;
plot(new_x,y_graph_trunc)

[Philippe Lebel]

I corrected an error (in the for loop). The index was going out of bounds in certain cases

[Ang Xian Jia]

Hey Phillippe,

Thanks for the help. I'm thinking of vertical stretching of second graph into same range of y for first graph(havent done) and horizontal stretching of second graph into same range of x for first graph(you had done it). Is that possible also?

Note: I have reuploaded the first graph data in much smaller file.

[Philippe Lebel]

how about that:

close all
clear
load('firstgraph_y_graph.mat') 
load('firstgraph_x_graph.mat') 
plot(x, y_graph);
hold on
max_first_graph_y = max(y_graph);
max_first_graph_x = max(x);

load('secondgraphdata.mat')

[max_1,index_1] = max(y_graph);
spacing = floor(length(y_graph)/3);
for i = 1:3
    offsets(i) = (i-1)*spacing;
    [maxes(i), indexes(i)] = max(y_graph((i-1)*spacing + 1:(i*spacing)));
end
indexes = indexes + offsets;
y_graph_trunc = y_graph(indexes(1):indexes(3));
ratio = max_first_graph_x / length(y_graph_trunc);
new_x = 1:ratio:max_first_graph_x;

y_offset = min(y_graph_trunc);
y_graph_trunc = y_graph_trunc - y_offset;
y_graph_trunc = y_graph_trunc * max_first_graph_y / max(y_graph_trunc);

plot(new_x,y_graph_trunc)

[Ang Xian Jia]

Hi Phillipee,

Is it possible to match those 3 peaks together also ?