In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time)
Matlab code for Discrete Wavelet Transform
%Read Input Image Input_Image=imread('rose.bmp'); %Red Component of Colour Image Red_Input_Image=Input_Image(:,:,1); %Green Component of Colour Image Green_Input_Image=Input_Image(:,:,2); %Blue Component of Colour Image Blue_Input_Image=Input_Image(:,:,3); %Apply Two Dimensional Discrete Wavelet Transform [LLr,LHr,HLr,HHr]=dwt2(Red_Input_Image,'haar'); [LLg,LHg,HLg,HHg]=dwt2(Green_Input_Image,'haar'); [LLb,LHb,HLb,HHb]=dwt2(Blue_Input_Image,'haar'); First_Level_Decomposition(:,:,1)=[LLr,LHr;HLr,HHr]; First_Level_Decomposition(:,:,2)=[LLg,LHg;HLg,HHg]; First_Level_Decomposition(:,:,3)=[LLb,LHb;HLb,HHb]; First_Level_Decomposition=uint8(First_Level_Decomposition); %Display Image subplot(1,2,1);imshow(Input_Image);title('Input Image'); subplot(1,2,2);imshow(First_Level_Decomposition,[]);title('First Level Decomposition');
Applications of DWT
The discrete wavelet transform has a huge number of applications in science, engineering, mathematics and computer science. Most notably, it is used for signal coding, to represent a discrete signal in a more redundant form, often as a preconditioning for data compression. Practical applications can also be found in signal processing of accelerations for Image recognition ,Image retrieval techniques in digital communications and many others
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