Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instantaneous frequency and wave shape functions (I)   Although one can formulate an intuitive notion of instantaneous frequency,
generalizing "frequency" as we understand it in e.g. the Fourier transform, a
rigorous mathematical definition is lacking. In this paper, we consider a class
of functions composed of waveforms that repeat nearly periodically, and for
which the instantaneous frequency can be given a rigorous meaning. We show that
Synchrosqueezing can be used to determine the instantaneous frequency of
functions in this class, even if the waveform is not harmonic, thus
generalizing earlier results for cosine wave functions. We also provide
real-life examples and discuss the advantages, for these examples, of
considering such non-harmonic waveforms.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys