A new form of the Fourier transform for time-varying frequency estimation

1995 ◽  
Vol 47 (2) ◽  
pp. 187-200 ◽  
Author(s):  
Vladimir Katkovnik
Keyword(s):  
Fourier Transform ◽  
Frequency Estimation ◽  
Time Varying ◽  
Time Varying Frequency ◽  
New Form ◽  
The Fourier Transform

scholarly journals Another approach to the evaluation of a certain multivariate compound distribution

2016 ◽  
Vol 24 (3) ◽  
pp. 339-349
Author(s):  
Elena-Gratiela Robe-Voinea ◽  
Raluca Vernic
Keyword(s):  
Fourier Transform ◽  
Probability Function ◽  
Probability Generating Function ◽  
Recursive Formula ◽  
Aggregate Model ◽  
Insurance Portfolio ◽  
Compound Distribution ◽  
Different Types ◽  
New Form ◽  
The Fourier Transform

AbstractIn this work, we consider the multivariate aggregate model introduced in [11], model that takes into account the case when different types of claims affect in the same time an insurance portfolio under some specific assumptions related to the number of claims. For the probability function of the corresponding multivariate compound distribution, [11] obtained an exact recursive formula proved using the properties of the probability generating function. In this paper, we present a new shorter proof of the same formula that we also extend to a new form. Moreover, we present an alternative approximate method to evaluate the compound distribution based on the Fourier transform, and we compare both methods on a numerical example.

Discrete Time, Discrete Frequency

2021 ◽  
pp. 106-155
Author(s):  
Victor Lazzarini
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Continuous Time ◽  
Time Varying ◽  
Discrete Frequency ◽  
The Fourier Transform ◽  
Definition Of ◽  
The Time Domain

This chapter is dedicated to exploring a form of the Fourier transform that can be applied to digital waveforms, the discrete Fourier transform (DFT). The theory is introduced and discussed as a modification to the continuous-time transform, alongside the concept of windowing in the time domain. The fast Fourier transform is explored as an efficient algorithm for the computation of the DFT. The operation of discrete-time convolution is presented as a straight application of the DFT in musical signal processing. The chapter closes with a detailed look at time-varying convolution, which extends the principles developed earlier. The conclusion expands the definition of spectrum once more.

scholarly journals Adaline-based approaches for time-varying frequency estimation in power systems

2009 ◽  
Vol 42 (19) ◽  
pp. 31-36 ◽  
Author(s):  
Damien Halbwachs ◽  
Patrice Wira ◽  
Jean Mercklé
Keyword(s):  
Power Systems ◽  
Frequency Estimation ◽  
Time Varying ◽  
Time Varying Frequency
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