In this work we examine a face recognition system based on advanced correlation filters. A thorough theoretical design analysis of, Minimum Average Correlation Energy (MACE) filters and Optimum Trade-off Synthetic Discriminant Function (OTSDF) also commonly known as Optimal Trade-off Filter (OTF) is provided. In practice one of the major computational aspects in the correlation filter design is...

The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFTs of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (...

In many signal processing applications, recent techniques often rely on the estimation of a probabilistic model. Many times, this model does not focus on the observed data itself, but rather on a spectral or time-frequency transform of this data, such as the discrete Fourier transform (DFT) or the short-time Fourier transform (STFT). A common statistical assumption regarding these transforms is...

With the knowledge of the syndromes Sa,b, 0 ≤ a, b ≤ q − 2, the exact error values cannot be determined by using the conventional (q − 1)2-point discrete Fourier transform in the decoding of a plane algebraic-geometric code over GF (q). In this letter, the inverse q-point 1-dimensional and q2-point 2dimensional affine Fourier transform over GF (q) are presented to be used to retrieve the actual...

Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonorm...

In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent functions, which we shall call (weak, strong) octa/hexa/2-bent functions. We investigate relationships between these classes and completely characterize the octabent and hexabent functions in terms of bent functions.

The proposed research paper shall analyze a method of image change detection based upon the Fractional Fourier transform (FrFT), which can provide results with good precision and better recall values obtained by optimizing its fractional order 'a'. The method is analyzed because, with extra degree of freedom provided by the Discrete Fractional Fourier Transform (DFrFT), we can get mor...

This paper establishes a product rule for fractional derivatives of a realvalued function defined on a finite dimensional Euclidean vector space. The proof uses Fourier transforms. MSC 2010 : Primary: 26A33, 26B12; Secondary: 60E07

Let Sωf = ∫ ω f̂(ξ)e ixξ dξ be the Fourier projection operator to an interval ω in the real line. Rubio de Francia’s Littlewood Paley inequality [31] states that for any collection of disjoint intervals Ω, we have ∥∥ [∑ ω∈Ω |Sωf | 1/2∥∥ p . ‖f‖p, 2 ≤ p <∞. We survey developments related to this inequality, including the higher dimensional case, and consequences for multipliers.

On the half line 0; 1) we study rst order diierential operators of the form B 1 i d dx + Q(x); where B := B 1 0 0 ?B 2 ; B 1 ; B 2 2 M(n; C) are self{adjoint positive deenite matrices and Q : R + ! M(2n; C); R + := 0; 1); is a continuous self{adjoint oo{diagonal matrix function. We determine the self{adjoint boundary conditions for these operators. We prove that for each such boundary value pro...