This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general natu...

In this paper, we derive linear complexity over Fp of the M -ary Sidel’nikov sequences using discrete Fourier transform. As an example, we represent the linear complexities of the ternary Sidel’nikov sequences. It turned out that the ternary Sidel’nikov sequences have the linear complexity nearly close to their periods.

The sensitivity conjecture is one of the central open problems in boolean complexity. A recent work of Gopalan et al. [CCC 2016] conjectured a robust analog of the sensitivity conjecture, which relates the decay of the Fourier mass of a boolean function to moments of its sensitivity. We prove this robust analog in this work.

Abstract: Integral expressions for positive-part moments E Xp + (p > 0) of random variables X are presented, in terms of the Fourier-Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-par...

A mathematical theory on the computational complexity of the Discrete Fourier Transform (DFT) is required, independently of any kind of known Fast Fourier Transform (FFT) algorithm.

This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). We demonstrate an approach to mitigating spectral leakage based on windowing...

Traditional Fast Fourier Transform algorithm makes the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is doubly selective (i.e. time-frequencyselective), this traditional methodology fails. Since the channel frequency response is rapidly time-varying as a result the optimal transmission/reception methodology no...

There are many motivations for the discrete Fourier transform. Those of you in computer science have probably encountered them first in signal processing and perhaps further in cool theory results like switching lemmas. Those of you in physics have definitely encountered the continuous fourier transform, most likely first in quantum theory where we learn that the fourier transform goes between ...

A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) of an input vector. Efficient means that the FFT computes the DFT of an n-element vector in O(n logn) operations in contrast to the O(n2) operations required for computing the DFT by definition. FFTs exist for any vector length n and for real and higher-dimensional data. Parallel FFTs have b...