Research Of DFT Algorithm Based On Multi-dimensional Vector Matrix

In today’s high-tech rapid development of information age, each field in theaspect of scientific research is progressing excellence. Because of the superiority oforthogonal transform algorithm, it has an extremely wide range of applications,including satellite laser ranging, multi-view video coding processing, artificial neuralnetworks to deal with noise and so on. Orthogonal transformation algorithmcomprises Fourier transform algorithm, discrete cosine transform algorithm, walshtransform algorithm and so on.Among them, the Fourier transform algorithm as a classical algorithm orthogonaltransformation is widely used. However, with the growing demand for dealing withmulti-dimensional signal，large amounts of data information and a large number ofredundant data, the demand for a more efficient orthogonal transform algorithm isincreasing.To solve this problem, we proposed an innovative multi-dimensional vectormatrix theory. Not only in the field of orthogonal transform algorithm it has been anunprecedented breakthrough, but also it breaks the limitations of the traditionaltwo-dimensional model. The concept of the matrix is extended to themulti-dimensional matrix. With this model, this paper will extend the classical Fouriertransform algorithm to the multi-dimensional field and presents a multi-dimensionaldiscrete Fourier transform algorithm.First, this paper introduces the definition of multi-dimensional vector matrix,based on this defines multi-dimensional complex matrix operations and lays thefoundation for future multi-dimensional data operations.Then, this paper studies centralized energy efficiency and orthogonal of themulti-dimensional Fourier transform nuclear matrix, deduces the formula, verifies theorthogonal of the formula with Matlab. All these have rigorously validated theeffectiveness of the algorithm. After this, the translational property of the Fourier transform is extended into multi-dimensional field and also proved. Through dealingwith three-dimensional simulation of the signal by the four-dimensional Fouriertransform nuclear matrix, it validates the effectiveness of the algorithm.Finally, the multi-dimensional vector Fourier transform and discrete cosinetransform is analyzed on the aspect of energy concentration. At first break themulti-dimensional video signal to corresponding blocks and restructure into a newarray, which is convenient to be dealt. Then with the help of Matlab and VC, thediscrete cosine transform and Fourier transform are applied to the signal respectively.The result of simulation shows that multi-dimensional discrete Fourier transformperformance better than discrete cosine transform in terms of energy concentration.So multi-dimensional discrete Fourier transform is suit to process the data which has alarge amount of information.