Study On Discrete Sine Transform Algorithm Based On Algebraic Signal Processing Theory

The main purpose of signal processing is to find a simple and effective transformation method and extract the important information contained in the signal.As the most basic method of signal processing,Discrete Fourier Transform plays an important role.But with the wide application of signal processing,simple Fourier transform can not meet the needs.Therefore,the research of discrete transform algorithm is of great significance in signal processing.In this paper,with the basic principles of algebraic signal processing,a signal model based on the generalized Chebyshev polynomial is established in the condition of translating operator and the generalized Chebyshev polynomials.In this model,The Discrete Sine Transformation matrixe is derived.The research work is as follows.?1?Based on the theory of algebraic signal processing,a classical signal model is constructed.The Discrete Fourier Transform matrix is derived from the finite signal model combined with the boundary conditions.In the simulation experiment,the Discrete Fourier Transform matrix of the model is used to extract the frequency of the sinusoidal signal.The results show that the Fourier transform matrix of the model can accurately extract the frequency of the signal.?2?According to the generalized Chebyshev polynomial,a signal model based on the generalized Chebyshev polynomial is established.In the one-dimensional finite signal model,it is found that the discrete transform matrixes are the three types of discrete sine transform,DST₁,DST₃ and DST₇.The simulation experiment shows that the discrete transform matrixes can also extract the signal frequency in the case of noise.Compared with the classical algebraic signal model,the error is relatively small.?3?According to the problem of large computational complexity of discrete sine transform matrix,an improvement based on Cooley-Tukey algorithm is proposed.Taking DST₁ as an example,split the odd and even two cases to discuss,Simulation experiments show that under the same signal length,the operation of the improved discrete sine transform algorithm is much less than that of the original discrete sine transformation algorithm,which improves the computation speed.