Antisymmetric Sequences Research Articles

Description of Pulse Sequences Containing Single Pulses and Binomial Sequences by Means of Rotation Operators

A general formalism is developed to describe the excitation behavior of pulse sequences in NMR experiments. In order to describe pulse sequences with constant or alternating pulse phases, spin echo, and phase-cycled sequences, pulse-sequence matrices are constructed by application of rotation matrices about the three coordinate axes in space. After generality is reduced to symmetric and antisymmetric sequences, conclusions are drawn about the general form of sequence matrices for sequences phase cycled by Exorcycle. The formalism is then employed for binomial sequences and spectral-editing sequences containing binomial sequences, and the analytical expressions obtained are used to simulate the excitation behavior of these sequences.

Prime-factor algorithm and winograd fourier transform algorithm for real symmetric and antisymmetric sequences

In the paper, algorithms for computing discrete Fourier transform (DFT) of 1-D real symmetric and antisymmetric sequences, using the prime-factor algorithm (PFA) and the Winograd Fourier transform algorithm (WFTA), are presented. These algorithms are obtained from different factorisations of the Fourier matrix, and it is shown that symmetry conditions exist at each stage which are used to construct efficient algorithms for computing DFTs.

Very fast computation of the radix-2 discrete Fourier transform

This paper develops and presents a radix-2 fast Fourier transform (FFT) algorithm that reduces the computational effort (as measured by the number of multiplications) to two-thirds of the effort required by most radix-2 algorithms. The resulting algorithm is similar to one obtained by applying a principle suggested by Rader and Brenner; however, its structure is particularly appealing when transforming pure real or imaginary sequences and/or symmetric or antisymmetric sequences; furthermore, memory requirements (other than those for storing the input data) do not grow with the size of the transform.