  Unambiguous detection of signals superimposed on unknown trends is difficult
for unevenly spaced data. Here, we formulate the Discrete Chi-square Method
(DCM) that can determine the best model for many signals superimposed on
arbitrary polynomial trends. DCM minimizes the Chi-square for the data in the
multi-dimensional tested frequency space. The required number of tested
frequency combinations remains manageable, because the method test statistic is
symmetric in this tested frequency space. With our known tested constant
frequency grid values, the non-linear DCM model becomes linear, and all results
become unambiguous. We test DCM with simulated data containing different
mixtures of signals and trends. DCM gives unambiguous results, if the signal
frequencies are not too close to each other, and none of the signals is too
weak. It relies on brute computational force, because all possible free
parameter combinations for all reasonable linear models are tested. DCM works
like winning a lottery by buying all lottery tickets. Anyone can reproduce all
our results with the DCM computer code. All files, variables and other program
code related items are printed in magenta colour. Our Appendix gives detailed
instructions for using dcm.py. We also present one preliminary real use case,
where DCM is applied to the observed (O) minus the computed (C) eclipse epochs
of a binary star, XZ And. This DCM analysis reveals evidence for the possible
presence of a third and a fourth body in this system. One recent study of a
very large sample of binary stars indicated that the probability for detecting
a fourth body from the O-C data of eclipsing binaries is only about 0.00005.
