Identification of safety-critical events using kinematic vehicle data and the discrete fourier transform

2016 ◽  
Vol 96 ◽  
pp. 162-168 ◽  
Author(s):  
Robert Kluger ◽  
Brian L. Smith ◽  
Hyungjun Park ◽  
Daniel J. Dailey
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Critical Events ◽  
Safety Critical ◽  
Vehicle Data

scholarly journals The Formalization of Discrete Fourier Transform in HOL

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiping Shi ◽  
Yupeng Zhang ◽  
Yong Guan ◽  
Liming Li ◽  
Jie Zhang
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Order Logic ◽  
Theorem Prover ◽  
Formal Definition ◽  
Accurate Analysis ◽  
Higher Order Logic ◽  
Safety Critical ◽  
Fundamental Properties ◽  
Definition Of

Traditionally, Discrete Fourier Transform (DFT) is performed with numerical or symbolic computation, which cannot guarantee 100% accurate analysis which may be necessary for safety-critical applications. Machine theorem proving is one of the formal methods that perform accurate analysis with completeness to some extent. This paper proposes the formalization of DFT in a higher-order logic theorem prover named HOL. We propose the formal definition of DFT and verify the fundamental properties of DFT. Two case studies are presented to illustrate usefulness and correctness of the formalized DFT, including formal verifications of Fast Fourier Transform (FFT) and cosine frequency shift.

APPLICATION OF UNCONVENTIONAL METHODS FOR FREQUENCY ANALYSIS IN ACOUSTICS

Akustika ◽  
2020 ◽  
Vol 36 (36) ◽  
pp. 25-32
Author(s):  
Jaroslav Smutný ◽  
Dušan Janoštík ◽  
Viktor Nohál
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Analysis ◽  
Mathematical Analysis ◽  
Measured Data ◽  
Application Area ◽  
Acoustic Response ◽  
Recommendations For Practice ◽  
Unconventional Methods ◽  
Frequency Area

The goal of this study is to familiarize a wider professional public with not fully known procedures suitable for processing measured data in the frequency area. Described is the use of the so-called Multi-taper method to analyze the acoustic response. This transformation belongs to a group of nonparametric methods outgoing from discrete Fourier transform, and this study includes its mathematical analysis and description. In addition, the use of respective method in a specific application area and recommendations for practice are described.

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