# How to find the maximum value of C that corresponds to a set of X,Y coordinates?

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Brianna Miranda on 29 Jul 2022
Commented: Star Strider on 29 Jul 2022
I have a spectrogram plot that contains X,Y and C. I want to find the maximum values of C from that spectrogram and also the XY coordinates that they correspond to. I have this so far but I am not sure how to get the X,Y coordinates that each value of max C corresponds to.
imagesc(X,Y,10*log10(C))
maxC = max(C);

Star Strider on 29 Jul 2022
The spectrogram plot is actually a surf plot with the view set to display it looking from the top, so the ‘Z’ values will give you all the information you want.
One way of getting that information from the spectrogram is to use the medfreq funciton. See Track Chirps in Audio Signal for an example.
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Star Strider on 29 Jul 2022
With a spectrogram, the ‘maximum’ can be defined as the maximum value of the ‘Z’ matrix (the eqay solution), or the maximum frequency with respect to time (the solution that the link I posted could be useful to find).
The maximum value of the ‘Z’ matrix is simply:
[r,c] = find(Z == max(Z(:))
so for example —
[X,Y] = ndgrid(1:0.1:5);
Z = randn(size(X))
Z = 41×41
-0.0639 -2.4202 -0.5892 -0.3153 -1.2375 0.2582 0.5664 -0.0020 -0.4781 -0.4400 0.3104 -1.6870 2.3617 0.1904 0.4709 0.5604 0.9655 1.4496 0.8379 1.5481 -0.2459 0.1577 2.6907 1.9585 -0.7600 0.8633 -0.0593 -0.0278 -0.7414 0.2447 -0.8915 -1.3448 -0.9731 1.4001 -1.4113 0.0759 -0.3949 1.0819 -1.2504 0.2395 -0.5119 0.4586 -0.9246 0.8510 1.2941 1.2805 -0.4253 -0.0403 1.7856 -1.3657 1.5380 -0.8891 -0.9842 0.6527 -2.5084 -1.8022 0.3371 1.2054 -0.6248 -0.9365 0.0217 0.7413 0.9703 -1.3422 -0.6889 2.4894 -0.8549 -0.4740 -0.2225 -0.5694 -2.0222 1.1507 -0.2375 -2.5342 0.8704 0.9467 -1.1114 -2.4286 -0.3480 -1.4527 0.8740 -0.5818 -1.1733 0.6569 1.0697 0.2519 -1.4657 0.9207 -0.5496 0.5370 -0.3532 0.4664 -1.1207 -0.2304 0.0524 -0.0722 0.3842 -0.5589 -1.0253 0.6298 -0.3426 -0.8348 -2.4134 1.7251 -2.4607 -1.6548 -0.1585 -1.3724 1.6503 -0.1679 -0.6309 -0.2147 -0.6524 0.7183 -2.7147 1.3611 1.0592 -0.5393 1.2776 0.6410 0.7345 -0.1412 1.6778 -0.8870 0.1101 -0.2241 0.2429 1.8206 -0.6441 1.5836 -0.6047 1.9053 1.9305 0.3951 0.5758 -1.3763 0.2552 -1.7303 -0.0525 3.0846 -1.0426 0.0874 -0.3216 0.1369 0.2692 1.2349 0.5056 -1.2016 -0.8287 -0.7030 -1.6341 -0.6052 0.1854 -0.5525 -1.5532 -1.9856 0.6408 1.9057 -1.3372 1.1240 -0.4402 -1.4120 -0.1029 -0.5735 -0.2999 -0.0698 1.8575 0.2400 1.4729 0.6123 -0.0452 0.4546 0.5246 0.8361 2.2197 -0.6524 -0.1364 0.8422 0.4287 -0.7655 0.6935 0.9505 -0.1121 -1.8347 -1.2506 -1.0413 1.2313 -0.0750 -0.9505 0.1271 -0.5988 -1.3527 1.5817 0.4073 0.0950 -0.1533 -1.4091 1.1605 -1.0842 -0.9306 -0.3523 -1.8747 0.3412 1.2081 -2.6801 0.1715 0.0911 -0.1921 -1.0078 0.3955 0.1917 -0.5632 1.3781 1.4707 -0.7444 -1.0536 -0.4651 -0.4820 1.1504 -0.2833 1.1034 -0.0543 -0.1905 -0.2366 -2.0467 -0.1114 1.0882 -0.2817 0.5707 -0.7683 -1.1562 -0.3642 -1.0025 -0.7422 0.3502 -1.0852 -0.1734 1.7628 -0.7464 -0.8762 -1.6987 -0.3549 1.3508 -1.3206 -1.7158 0.6468 1.0099 -0.2371 0.2916 0.0334 0.3175 0.2897 -0.3463 1.5408 2.0720 0.1516 0.3823 -1.3584 1.1463 0.2069 1.2317 0.2429 1.4249 -0.0526 0.5708 -0.0585 0.1757 1.1555 -0.0869 -0.3246 1.1156 -0.5752 0.8764 -1.7859 -1.9668 -0.8118 0.0052 -1.3435 -0.5732 0.7530 -0.3858 0.0806 -0.7766 0.4792 2.5190 -0.6782 -1.3124 -0.4009 -1.7604 0.2375 -1.4506 0.9221 -0.9909 -0.3864 -0.5869 -0.0340 -1.1347 1.2365 -0.0547 -0.7845
[r,c] = find(Z == max(Z(:)))
r = 13
c = 9
maxZ = Z(r,c)
maxZ = 3.2838
figure
surf(X,Y,Z)
hold on
stem3(X(r,c),Y(r,c),Z(r,c), '^r', 'MarkerFaceColor','r')
hold off
grid on
.

Voss on 29 Jul 2022
X = 1:3:31;
Y = 1:2:13;
C = rand(numel(Y),numel(X));
imagesc(X,Y,10*log10(C))
[maxC,idx] = max(C(:))
maxC = 0.9986
idx = 58
[yidx,xidx] = ind2sub(size(C),idx)
yidx = 2
xidx = 9
maxX = X(xidx)
maxX = 25
maxY = Y(yidx)
maxY = 3
line(maxX,maxY,'Marker','x','MarkerEdgeColor','r')

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