This paper is about a new efficient method for the implementation of convolvers and correlators using the Fermat Number Transform (FNT) and the inverse (IFNT). The latter present advantages compared to Inverse Fast Fourier Transform (IFFT). An efficient state space method for implementing the Inverse FNT (IFNT) over rectangular windows is proposed for the cases where there is a large overlap be...

Matrices equivariant under a group of permutation matrices are considered. Such matrices typically arise in numerical applications where the computational domain exhibits geometrical symmetries. In these cases, group representation theory provides a powerful tool for block diagonalizing the matrix via the Generalized Fourier Transform. This technique yields substantial computational savings in ...

This brief explores the connections between nonuniform sampling of a certain function and the almost periodic extension of its Fourier transform. It is shown that the Fourier transform of a bandlimited function can be extended (as a weighted sum of translates) as a Stepanoff almost periodic function, to the whole frequency axis. This result leads to a generalized nonuniform sampling theorem whi...

An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal. Subsequently, attention is focused on the special case of the...

FRACTIONAL FOURIER INTEGRAL THEOREM AND FRACTIONAL FOURIER SINE AND COSINE TRANSFORM Saleem Iqbal, S.M. Raza, * LalaRukh Kamal and Farhana Sarwar Department of Mathematics/Physics, University of Balochistan, Quetta, Pakistan e-mail: fs1005,saleemiqbal81,[email protected]. ABSTRACT: The fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform (FT). Recently...

This brief explores the connections between nonuniform sampling of a certain function and the almost periodic extension of its Fourier transform. It is shown that the Fourier transform of a band-limited function can be extended (as a weighted sum of translates) as a Stepanoff almost periodic function to the whole frequency axis. This result leads to a generalized nonuniform sampling theorem whi...

The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform....

The sensitivity against outliers due to undetected noise bursts often limits the performance of adaptive filters in applications where especially fast convergence is required, as, for example, in adaptive beamforming for audio signal acquisition or in acoustic echo cancellation. In this paper, we analyze the problem of outliers for a robust generalized sidelobe canceler (RGSC) in the discrete F...

Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Perio...