Transform Domain Characterization Research Articles

Weak nonhomogeneous wavelet dual frames for Walsh reducing subspace of L2(ℝ+)

In wavelet analysis, refinable functions are the bases of extension principles for constructing (weak) dual wavelet frames for [Formula: see text] and its reducing subspaces. This paper addresses refinable function-based dual wavelet frames construction in Walsh reducing subspaces of [Formula: see text]. We obtain a Walsh–Fourier transform domain characterization for weak [Formula: see text]-adic nonhomogeneous dual wavelet frames; and present a mixed oblique extension principle for constructing weak [Formula: see text]-adic nonhomogeneous dual wavelet frames in Walsh reducing subspaces of [Formula: see text].

Weak Gabor bi-frames on discrete periodic sets

Due to its good potential for digital signal processing, discrete Gabor analysis has received broad interests in recent years. This paper addresses Gabor analysis on a general discrete periodicsubset $S$ of $\bb~Z$. It is well known that the projections of Gabor frames for $l^2(\bb~Z)$ onto $l^2(S)$ cannot cover all Gabor frames for $l^2(S)$ if $S\neq{\bb~Z}$. In this paper, we introduce the notion of weak Gabor bi-frame (WGBF) which generalizes the one of Gabor bi-frame. We obtain a Zak transform domain characterization and a time domain characterization of WGBF in $l^2(S)$.The obtained results are new even if $S=\bb~Z$. Some examples are provided.

Transform Domain Characterization of Dual Group Codes of Cyclic Group Codes over Elementary Abelian Groups

The group of characters of an elementary Abelian group has been used to define duality between its subgroups, which in turn is extended to duality between group codes. The transform domain description of the dual codes of cyclic group codes of length over has been developed in this paper. Several example codes and their duals have been presented also.

Eigensignals of Downsamplers in Time and Transform Domains

As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system. An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient. In this paper, the eigensignals are studied and characterized in the time and z domains. The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambert-form series are used for the transform-domain characterization. Examples of non-trivial eigensignals are provided. These include the special classes of multiplicative and completely multiplicative eigensignals. Moreover, the locus of poles of eigensignals with rational z transforms are identified.

DFT for cyclic code overF p +uF p + ··· +u k-1 F p

The transform domain characterization of cyclic codes over finite fields using Discrete Fourier Transform(DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for cyclic codes overFp +uFp+ ··· +uk-1Fp. We give a way to characterize cyclic codes overFp +uFp+ ··· +uk-1Fp by Mattson-Solomon polynomials and multiple defining sets.

Transform domain approach for sequence design and its applications

Many communication and radar systems necessitate the use of sequences with desired autocorrelation (AC) and cross-correlation (CC) properties. This paper presents a systematic method based on the transform domain characterization of the AC and CC constraints to generate new families of sequences that meet the requirements. We demonstrate that some existing families can easily be generated by our approach. Our approach, however, renders new families of sequences with less constraints. The proposed approach is elementary and can easily be extended to synthesize two-dimensional arrays or even higher dimensional waveforms that possess the desired multidimensional correlation properties. A preamble structure based on our new sequence family is suggested and performance of frequency offset and channel estimation algorithms for a multiantenna orthogonal frequency-division multiplexing (OFDM) system that uses such a preamble is given.

Fq-linear Cyclic Codes over $$F{_q^m}$$ : DFT Approach

Codes over Fqm that are closed under addition, and multiplication with elements from Fq are called Fq-linear codes over Fqm. For m ≠ 1, this class of codes is a subclass of nonlinear codes. Among Fq-linear codes, we consider only cyclic codes and call them Fq-linear cyclic codes (FqLC codes) over Fqm. The class of FqLC codes includes as special cases (i) group cyclic codes over elementary abelian groups (q = p, a prime), (ii) subspace subcodes of Reed-Solomon codes (n = qm - 1) studied by Hattori, McEliece and Solomon, (iii) linear cyclic codes over Fq (m = 1) and (iv) twisted BCH codes. Moreover, with respect to any particular Fq-basis of Fqm, any FqLC code over Fqm can be viewed as an m-quasi-cyclic code of length mn over Fq. In this correspondence, we obtain transform domain characterization of FqLC codes, using Discrete Fourier Transform (DFT) over an extension field of Fqm. The characterization is in terms of any decomposition of the code into certain subcodes and linearized polynomials over Fqm. We show how one can use this transform domain characterization to obtain a minimum distance bound for the corresponding quasi-cyclic code. We also prove nonexistence of self dual FqLC codes and self dual quasi-cyclic codes of certain parameters using the transform domain characterization.

DFT Domain Characterization of Quasi-Cyclic Codes

The transform domain characterization of linear cyclic codes over finite fields using Discrete Fourier Transform (DFT) over an appropriate extension field is well known. In this paper, we extend this transform domain characterization for linear quasi-cyclic codes over finite fields. We show how one can derive a lower bound on the minimum Hamming distance of a quasi-cyclic code and decode the code upto that minimum Hamming distance using this characterization.

Transform domain characterization of cyclic codes overZ m

Cyclic codes with symbols from a residue class integer ringZm are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring ofZm. It is shown that a cyclic code of length n overZm,n relatively prime tom, consists ofn-tuples overZm having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. Whenm is equal to a product of distinct primes every cyclic code overZm has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs overZm are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes overZm are obtained and nonexistence of self-dual codes for certain values ofm is proved.