Listing values ​​for a specific harmonic line from waterfall figure

Hello dear Matlab team,

I would like to ask you how to gate listing values ​​for a specific harmonic line from waterfall figure?

I have this waterfall figure below:

It is transpose to imagesc see in following figure:

And I would like to ask you how I can data for specific harmonic line in this figure?

Thank you,

Best regards,

Jan

Answer 1

[Star Strider]

By 'harmonic line', I assume you intend frequency, the x-axis coordinate in each plot. A waterfall plot is a specific depiction of a matrix. I use surf here for convenience.

If the one you want matches exactly a frequency in plot, and the frequencies map to the x-axis coordinate exactly (as the columns of the plotted matrix), you can probably just use 'logical indexing' to get them.

However, the easiest way woukld be to use the scatteredInterpolant function. The desired frequency can be anything with in the frequency range. The lines can either be constant with respect to one variable, or vary, as depicted by the 'Diagnoal Line' drawn here. I drew 'DiagonalLine' as a linear relation between 'Frequency' and 'Rotor Speed', however it does not havve to be linear and can be anything that works with the original data.

Example --

rsv = (0:0.5:8).';
frqv = (0:0.5:10).';
[Fm,RSm] = ndgrid(frqv, rsv);
Data = exp(-((Fm-2).^2/4.5+(RSm-6).^2)/3.5);
% disp(Data)


FRS = scatteredInterpolant(Fm(:), RSm(:), Data(:))

FRS = 
  scatteredInterpolant with properties:

                 Points: [357×2 double]
                 Values: [357×1 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

RotorSpeed_Frequency_2pi = FRS(frqv, ones(size(frqv))*2*pi)

RotorSpeed_Frequency_2pi = 21×1

0.7454 0.8330 0.9018 0.9458 0.9610 0.9458 0.9018 0.8330 0.7454 0.6462 0.5427 0.4415 0.3479 0.2657 0.1965

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RotorSpeed_Frequency_pi = FRS(frqv, ones(size(frqv))*pi)

RotorSpeed_Frequency_pi = 21×1

0.0793 0.0887 0.0960 0.1007 0.1023 0.1007 0.0960 0.0887 0.0793 0.0688 0.0578 0.0470 0.0370 0.0283 0.0209

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●

RSvF = frqv*1.1 + 0.5;

DiagonalLine = FRS(frqv, RSvF)

DiagonalLine = 21×1

0.0001 0.0009 0.0042 0.0160 0.0487 0.1201 0.2425 0.4020 0.5479 0.6140 0.5647 0.4195 0.2558 0.1282 0.0479

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figure
surf(Fm, RSm,Data, FaceAlpha=0.4, EdgeAlpha=0.5, DisplayName='Frequency-Rotor Speed Surface')
xlabel('Frequency')
ylabel('Rotor Speed')
colormap(turbo)
hold on
plot3(frqv, ones(size(frqv))*pi, RotorSpeed_Frequency_pi, '-b', LineWidth=2, DisplayName='Frequency=\pi')
plot3(frqv, ones(size(frqv))*2*pi, RotorSpeed_Frequency_2pi, '-r', LineWidth=2, DisplayName='Frequency=2\pi')
plot3(frqv, RSvF, DiagonalLine, '-m', LineWidth=2, DisplayName='Diagonal Line')
hold off
legend(Location='best')
axis([0  10    0  8])
view(50,45)

.

EDIT -- (29 Aug 2025 at 17:01)

Added 'Diagonal Line', added to discussion, tweaked code.

.

[Jan]

Hello,

Thank you very much for your update. If I understand right, you define interpolating function FRS by this line:

FRS = scatteredInterpolant(Fm(:), RSm(:), Data(:))

Subsequently, you are defining the line equation (slope of a line) which you want to show in data by:

RSvF = frqv*1.1 + 0.5

I did provide extending you're your script by 3 diagonal lines defined by equations only for my better understanding:

RSvF_1 = frqv*1;

RSvF_2 = frqv*0.5;

RSvF_3 = frqv*2;

DiagonalLine_1 = FRS(frqv,RSvF_1)

DiagonalLine_2 = FRS(frqv,RSvF_2)

DiagonalLine_3 = FRS(frqv,RSvF_3)

figure()

surf(Fm, RSm,Data, FaceAlpha=0.4, EdgeAlpha=0.5, DisplayName='Frequency-Rotor Speed Surface')

xlabel('Frequency')

ylabel('Rotor Speed')

colormap(turbo)

hold on

plot3(frqv, ones(size(frqv))*pi, RotorSpeed_Frequency_pi, '-b', LineWidth=2, DisplayName='Frequency=\pi')

plot3(frqv, ones(size(frqv))*2*pi, RotorSpeed_Frequency_2pi, '-r', LineWidth=2, DisplayName='Frequency=2\pi')

plot3(frqv, RSvF_1, DiagonalLine_1, '-m', LineWidth=2, DisplayName='Diagonal Line 1')

plot3(frqv, RSvF_2, DiagonalLine_2, '-c', LineWidth=2, DisplayName='Diagonal Line 2')

plot3(frqv, RSvF_3, DiagonalLine_3, '-y', LineWidth=2, DisplayName='Diagonal Line 3')

hold off

legend(Location='best')

axis([0 10 0 8])

view(50,45)

and I made showing this data by:

figure()

subplot(3,1,1)

plot(Fm(:,1) ,DiagonalLine_1)

xlabel('Rotor Speed (rad/s')

ylabel('Amplitude')

subplot(3,1,2)

plot(Fm(:,1) ,DiagonalLine_2)

xlabel('Rotor Speed (rad/s')

ylabel('Amplitude')

subplot(3,1,3)

plot(Fm(:,1) ,DiagonalLine_3)

xlabel('Rotor Speed (rad/s')

ylabel('Amplitude')

Potentially, I would like to ask you if is possible to avoid interpolating function scatteredInterpolant or not in this case for achieving the data based on typical electrical machine harmonic lines?? Because your generated data has positive values only but line interpolated data have positive and negative values becasue I want to avoid wrong data interpretation.

[Star Strider]

My pleasure!

The interpolation is actually correct. For 'DiagonalLine_3', it only fits to the frequency ('frqv') between 0 and 4. Beyond that, it extrapolates. You can experiment with the ExtrapolationMethod name-value pair to get the result you want. (The defailt is 'linear'.)

It would help to have your actual matrix, as well as a description of 'harmonic line', since I am unfamiliar with the term. (I guessed that it was a specific frequency, however I am not certain.) I would use the scatteredInterpolant function regardless, however the correct definition of 'harmonic line' and having your matrix to work with would be extremely helptul.

Example --

rsv = (0:0.5:8).';
frqv = (0:0.5:10).';
[Fm,RSm] = ndgrid(frqv, rsv);
Data = exp(-((Fm-2).^2/4.5+(RSm-6).^2)/3.5);
% disp(Data)


FRS = scatteredInterpolant(Fm(:), RSm(:), Data(:))

FRS = 
  scatteredInterpolant with properties:

                 Points: [357×2 double]
                 Values: [357×1 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

% RotorSpeed_Frequency_2pi = FRS(frqv, ones(size(frqv))*2*pi)
% RotorSpeed_Frequency_pi = FRS(frqv, ones(size(frqv))*pi)

RSvF = frqv*1.1 + 0.5;

DiagonalLine = FRS(frqv, RSvF);

RSvF_1 = frqv*1;
RSvF_2 = frqv*0.5;
RSvF_3 = frqv*2;
DiagonalLine_1 = FRS(frqv,RSvF_1)

DiagonalLine_1 = 21×1

0.0000 0.0002 0.0007 0.0030 0.0103 0.0297 0.0717 0.1454 0.2474 0.3536 0.4244 0.4278 0.3621 0.2574 0.1537

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DiagonalLine_2 = FRS(frqv,RSvF_2)

DiagonalLine_2 = 21×1

0.0000 0.0001 0.0002 0.0005 0.0008 0.0019 0.0029 0.0058 0.0080 0.0136 0.0171 0.0245 0.0277 0.0337 0.0343

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DiagonalLine_3 = FRS(frqv,RSvF_3)

DiagonalLine_3 = 21×1

0.0000 0.0007 0.0097 0.0752 0.3189 0.7396 0.9385 0.6514 0.2474 -0.0631 -0.2880 -0.4274 -0.4909 -0.4941 -0.4551

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figure()
% surf(Fm, RSm,Data, FaceAlpha=0.4, EdgeAlpha=0.5, DisplayName='Frequency-Rotor Speed Surface')
surf(Fm, RSm, zeros(size(Fm)), FaceColor=[1 1 1]*0.5)
xlabel('Frequency')
ylabel('Rotor Speed')
colormap(turbo)
hold on
% % plot3(frqv, ones(size(frqv))*pi, RotorSpeed_Frequency_pi, '-b', LineWidth=2, DisplayName='Frequency=\pi')
% % plot3(frqv, ones(size(frqv))*2*pi, RotorSpeed_Frequency_2pi, '-r', LineWidth=2, DisplayName='Frequency=2\pi')
% plot3(frqv, RSvF_1, DiagonalLine_1, '-m', LineWidth=2, DisplayName='Diagonal Line 1')
% plot3(frqv, RSvF_2, DiagonalLine_2, '-c', LineWidth=2, DisplayName='Diagonal Line 2')
plot3(frqv, RSvF_3, DiagonalLine_3, '-y', LineWidth=2, DisplayName='Diagonal Line 3')
plot(frqv(frqv<=4), RSvF_3(frqv<=4), '-k', LineWidth=6)
hold off
legend(Location='best')
axis([0  10    0  8])
% view(50,45)
view(0,90)                          % Top-Down View
grid on

 
% and I made showing this data by:
figure()
subplot(3,1,1)
% plot(Fm(:,1) ,DiagonalLine_1)
plot(frqv, DiagonalLine_1)
xlabel('Rotor Speed (rad/s')
ylabel('Amplitude')
subplot(3,1,2)
% plot(Fm(:,1) ,DiagonalLine_2)
plot(frqv, DiagonalLine_2)
xlabel('Rotor Speed (rad/s')
ylabel('Amplitude')
subplot(3,1,3)
% plot(Fm(:,1) ,DiagonalLine_3)
DiagonalLine_3(frqv>4) = NaN;               % Eliminate Extrapolated Values
plot(frqv, DiagonalLine_3)
xlabel('Rotor Speed (rad/s')
ylabel('Amplitude')
xlim([min(frqv) max(frqv)])

return

figure
surf(Fm, RSm,Data, FaceAlpha=0.4, EdgeAlpha=0.5, DisplayName='Frequency-Rotor Speed Surface')
xlabel('Frequency')
ylabel('Rotor Speed')
colormap(turbo)
hold on
plot3(frqv, ones(size(frqv))*pi, RotorSpeed_Frequency_pi, '-b', LineWidth=2, DisplayName='Frequency=\pi')
plot3(frqv, ones(size(frqv))*2*pi, RotorSpeed_Frequency_2pi, '-r', LineWidth=2, DisplayName='Frequency=2\pi')
plot3(frqv, RSvF, DiagonalLine, '-m', LineWidth=2, DisplayName='Diagonal Line')
hold off
legend(Location='best')
axis([0  10    0  8])
view(50,45)

.

[Jan]

ok, thank you very much for this support. I tested the ExtrapolationMethod based on link: scatteredInterpolant - Interpolate 2-D or 3-D scattered data - MATLAB

on other hand, harmonic line data are practically good based on this script.

I try to apply for my big data analysis. Thank you very much 😊

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.