Research On Discrete Cosine Transform Algorithm Based On Algebraic Signal Processing

Signal processing is a general term for the process of extracting and analyzing signals recorded on the media by means of transformation.The classical Fourier transform,as the most basic transform algorithm,has been applied in many signal processing techniques.However,with the diversity of signals,a single Fourier transform algorithm can no laonger meet the needs of signal processing,so it is necessary to derive a new transform algorithm.In the theoretical framework of algebraic signal processing,this paper establishes a new signal model,deduces the discrete transform algorithm under different models,and simulation experiments are carried out to analyze the actual application effect of the algorithm.The main work of the thesis includes the following contents:(1)Based on the spatial signal model,this paper defines a new translation operation and constructs a signal model based on the first kind of generalized Chebyshev polynomial.In the finite-dimensional signal model,the appropriate boundary conditions are selected and the transformation algorithm under the corresponding conditions is derived.Then the algorithm is applied to the experiment of one-dimensional signal and two-dimensional image,and is compared with the classical Fourier transform algorithm to analyze the effect of the algorithm on signal processing.(2)Based on the finite dimension signal model,the mathematical model and the new transformation algorithm of signal under polynomial extension are derived.In the experiment of denoising processing of noisy images,the new transform algorithm is compared with the traditional discrete cosine transform to analyze the denoising effect of the new transform algorithm on the noisy image.(3)In order to solve the problem that the new transform algorithm has a large amount of computation,an improved algorithm for discrete cosine transform is derived based on cooley-tukey fast algorithm.By comparing the operation amount before and after the algorithm improvement,it shows that the improved algorithm can effectively reduce the operation amount and improve the operation speed.