Inconsistent energy calculation using tcoeffs.m for time coefficients

[grigorishat]

Inconsistent energy calculation using tcoeffs.m for time coefficients

I've encountered an inconsistency when calculating the energy using the expansion coefficients computed by tcoeffs.m. The results do not match the expected scaling of A. However, when I perform the calculation with an overlap of nfft-1, it works as expected.

It seems that the time coefficients obtained from tcoeffs.m are not scaled in the same way as the array A. Below is an example code I used to compare the eigenvalues and the expansion coefficients for a specific mode and frequency:

NMODE = 10;
FREQNUM = 9;

% Display the corresponding eigenvalue
disp(L(FREQNUM, NMODE));

% Extract the expansion coefficients for the given mode and frequency
a_fm = a(FREQNUM,NMODE,:);

% Calculate and display the mean squared of the expansion coefficients
disp(mean(a(FREQNUM,NMODE,:) .* conj(a(FREQNUM,NMODE,:))));

% Compare with the scaling of A
disp(mean(A(FREQNUM,NMODE,:) .* conj(A(FREQNUM,NMODE,:))));

Using the code example_8_invspod.m with only 500 snapshots, nDFT=16 and nOvlp=15 for faster calculation, this gives the following values:

1.7836e-08

6.7273e-04

1.7836e-08

The scaling of the results from tcoeffs.m seems to differ from that of the array A, and the energy calculation yields inconsistent results. Any help or clarification on how to resolve this scaling issue would be greatly appreciated.