Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation (H-transformation) of a standard normal distribution (or, more general, of a symmetric distribution) Z and allow...

The high peak-to-average power ratio (PAPR) of the transmitted signal is a major drawback of multicarrier transmission such as orthogonal frequency-division multiplexing OFDM. A plethora of PAPR reduction techniques has been reported in the literature. Some of the techniques modify the phase and/or amplitude of symbols in the original symbol alphabet (SA) such as selected mapping and partial tr...

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebra...

The goals of the research discussed in this report are to determine the impact of di erent Cooley-Tukey decompositions on the performance of computer programs that compute the FFT, evaluate di erent methods for nding the most e cient decompositions, and determine the characteristics of the most e cient decompositions. Experiments are conducted using three di erent FFT programs and three dynamic...

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 (...