Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear analysis of the 4-step Carr\'e phase shifting algorithm:
  spectrum, signal-to-noise ratio, and harmonics response   We analyze the nonlinear Carr\'e 4-steps algorithm including its frequency
response, signal-to-noise ratio, and harmonics rejection using linear systems
theory. At first sight the previous statement as well as the title of this
paper seems paradoxical. How can we analyze the 4-step non-linear Carr\'e Phase
Shifting Algorithm (PSA) using linear system theory? The short answer is that
the non-linear Carr\'e algorithm may be decomposed into two building blocks.
The first block is a tunable linear 4-step PSA, and the second one is a
non-linear phase-step estimator. Although this fact is well known from the
derivation of the Carr\'e algorithm, nobody has properly exploited it. In other
words, to this day, we do not have explicit mathematical formulae for a) the
spectrum, b) the harmonics rejection, and c) the signal-to-noise ratio of the
non-linear Carr\'e algorithm. These are the properties of the Carr\'e's PSA
that we show here with novel and explicit mathematical formulae.

19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ