Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal Analysis of Continuous-time Systems using Fourier Transform   To study the dynamical behaviour of the engineering and physical systems, we
often need to capture their continuous behaviour, which is modeled using
differential equations, and perform the frequency-domain analysis of these
systems. Traditionally, Fourier transform methods are used to perform this
frequency domain analysis using paper-and-pencil based analytical techniques or
computer simulations. However, both of these methods are error prone and thus
are not suitable for analyzing systems used in safety-critical domains, like
medicine and transportation. In order to provide an accurate alternative, we
propose to use higher-order-logic theorem proving to conduct the frequency
domain analysis of these systems. For this purpose, the paper presents a
higher-order-logic formalization of Fourier transform using the HOL-Light
theorem prover. In particular, we use the higher-order-logic based
formalizations of differential, integral, transcendental and topological
theories of multivariable calculus to formally define Fourier transform and
reason about the correctness of its classical properties, such as existence,
linearity, time shifting, frequency shifting, modulation, time scaling, time
reversal and differentiation in time domain, and its relationships with Fourier
Cosine, Fourier Sine and Laplace transforms. We use our proposed formalization
for the formal verification of the frequency response of a generic n-order
linear system, an audio equalizer and a MEMs accelerometer, using the HOL-Light
theorem prover.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg