OFDM is a powerful multicarrier transmission technique used extensively for wireless applications. High PAPR is one of the deleterious problems of OFDM. This paper reviews basic OFDM system and PAPR problem associated with it. Also, the construction of M-QAM particularly 16-QAM sequences using QPSK Golay sequences over 4  is conferred. It is elucidated that a 16-QAM constellation can be writte...

The Savitzky–Golay smoothing and differentiation filter optimally fits a set of data points to a polynomial in the least-squares sense. The Savitzky–Golay filter has been developed and generalized well in the literatures. However, the data subset is subject to an odd number ð2m þ 1Þ: In this communication, the Savitzky–Golay filter is extended for even number data. Simulations are performed to ...

We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F2+uF2+vF2+uvF2 of length 6 and size 212. Writing a typical generating matrix of the form [I3|A], with A being a 3× 3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the gene...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...