Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Notes on the Use of the Windowed Fourier Transform for Spectral
  Analysis of Discretely Sampled Data   The properties of the Gabor and Morlet transforms are examined with respect
to the Fourier analysis of discretely sampled data. Forward and inverse
transform pairs based on a fixed window with uniform sampling of the frequency
axis can satisfy numerically the energy and reconstruction theorems; however,
transform pairs based on a variable window or nonuniform frequency sampling in
general do not. Instead of selecting the shape of the window as some function
of the central frequency, we propose constructing a single window with unit
energy from an arbitrary set of windows which is applied over the entire
frequency axis. By virtue of using a fixed window with uniform frequency
sampling, such a transform satisfies the energy and reconstruction theorems.
The shape of the window can be tailored to meet the requirements of the
investigator in terms of time/frequency resolution. The algorithm extends
naturally to the case of nonuniform signal sampling without modification beyond
identification of the Nyquist interval.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat