2) D **Discrete** **Wavelet** **Transform**: The **Discrete** Wavelets **Transform** (DWT) [39], transforms a **discrete** time signal to a **discrete** **wavelet** representation. Initially, the **wavelet** parameters are discretized to reduce the continuous basis set of wavelets to a **discrete** and orthogonal/ orthonormal set of basis wavelets. The 1D DWT is given as the inner product of the signal x(t) being transformed with each of the **discrete** basis functions.

Chui, Charles (1992) et al. [6] discusses the similarities and dissimilarities between Fourier and **Wavelet** **transform**. The fast Fourier **transform** (FFT) and the **discrete** **wavelet** **transform** (DWT) are both linear operations and the mathematical properties of the matrices involved in the transforms are similar as well. The inverse **transform** matrix for both the FFT and the DWT is the transpose of the original. As a result, both transforms can be viewed as a rotation in function space to a different domain. For the FFT, this new domain contains basis functions that are sine’s and cosines. For the **wavelet** **transform**, this new domain contains more complicated basis functions called wavelets, mother wavelets, or analysing wavelets. Both transforms have another similarity. The basis functions are localized in frequency, making mathematical tools such as power spectra (how much power is contained in a frequency interval) and scale grams (to be defined later) useful at picking out frequencies and calculating power distributions. The most interesting dissimilarity between these two kinds of transforms is that individual **wavelet** functions are localized in space. Fourier sine and cosine functions are not. This localization feature, along with wavelets' localization of frequency, makes many functions and operators using wavelets "sparse" when transformed into the **wavelet** domain. This sparseness, in turn, results in a number of useful applications such as data compression, detecting features in images, and removing noise.

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There will be a total of J estimations of the illuminant colour resulted from J -level DWT decomposition. However, selecting the correct estimation is not trivial. When the **wavelet** coefficients at finer scale j − 1 provides statistically strong features for illuminant colour estimation, due to the nature of **discrete** **wavelet** **transform**, one expects the similar estimation at very coarse scale j. Meanwhile, the estimation in finer scale is more prone to errors caused from fluctuations on **wavelet** coefficients. Due to multiscale decomposition, it is expected that the illuminant colour estimation at scale j is similar to the estimation at scale j − 1. Thus the difference in illuminant colour estimations between consecutive scales can be used to select the optimum scale where the estimations in consecutive scales, i.e., j and j − 1, have minimum angular error. The difference δ j,j−1 between two normalized illuminant colour estimations ˆ e j and ˆ e j−1 from scales j and

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Digital media can be copied and modified easily so protecting the copyright of digital media has become an important task. The digital watermark is introduced to solve the problem of copyright. The digital watermarking is a technique of embedding any watermark image into cover image using some known algorithm depending upon the requirement in multimedia data to identify the owner of the document[1].There are two common methods for watermarking: spatial domain and **transform** domain. In spatial domain pixels of an image are modified depending upon perceptual analysis of an image. But in **transform** domain some frequencies are selected and modified from their original values according to certain rules. The **transform** domain methods are more popular because watermark embedding is more robust in this domain as compared to spatial domain. It also provides more security and imperceptibility [3-5].In this paper we propose the watermarking scheme based on DWT (**discrete** **wavelet** **transform**) which works in **transform** domain. Watermarking algorithms are divided into two groups based on extraction: Blind and Non-blind watermarking. In blind watermarking extraction does not need original image but in non-blind watermarking original image is needed in watermark extraction [5].We use non-blind watermarking in this paper. The paper is organized as follows. Section 2 contains watermarking scheme DWT .Section 3 and 4 contain proposed algorithms and section 5 contains experimental results.

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Basically the medical images need more accuracy without loosing of information. The **Discrete** **Wavelet** **Transform** (DWT) was based on time-scale representation, which provides efficient multi- resolution. The lifting based scheme (9, 7) (The high pass filter has five taps and the low pass filter has three taps) filter give lossless mode of information. A more efficient approach to lossless whose coefficients are exactly represented by finite precision numbers allows for truly lossless encoding.

A watermark is a form, image or text that is impressed onto paper, which provides evidence of its authenticity. Digital watermarking is an extension of the same concept. There are two types of watermarks: visible watermark and invisible watermark. This project concentrates on implementing watermark in video. The main consideration for any watermarking scheme is its robustness to various attacks. Watermarking dependency on the original image increases its robustness but at the same time watermark should be made imperceptible. In this project, a robust video watermarking scheme using **discrete** **wavelet** **transform** (DWT) domain is proposed. The quality of the watermarked video is enhanced by using **wavelet** **transform**. Experimental results demonstrate that it is robust by calculating the peak signal to noise ratio (PSNR) between the watermark image and extracted image.

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Abstract—This paper presents the **Discrete** **Wavelet** **Transform** (DWT) for real-world speech compression design by using the Field Programmable Gate Array (FPGA) device. Compared with many reports which only focused on the DWT architecture design, this paper gives the speech compression system design detail on how to interface DWT block with SDRAM and audio codec chip. Speech compression was achieved by keeping only the approximation part of the DWT result. The compressed speech signal was read back after upsampling was performed. The resulting compressed speech can be heard clearly with some introduced background noise Future work is to reduce noise.

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Fundamentally the medicinal imaging transfers on more precision without much data misfortune. The **Discrete** **Wavelet** **Transform** (DWT) is set up on time-scale reintroduction, which outfits powerful multi- resolution.This work learns that the picture pixel values given to the DWT operation which gives way the high pass and low pass coefficients of the input picture less engineering plan contrast with the customary usage of the DWT can de accomplished, little change changes expands the throughput contrast with that of the past strategies The recreation consequences of DWT were acknowledged with the suitable test cases. Once the useful check is done, **discrete** **wavelet** change is blended by utilizing Xilinx device.

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A high-speed and reduced-area lifting architecture for 2D **Discrete** **Wavelet** **Transform** computation and the 2-D DWT Image Decomposition is proposed in this work. Lift scheme is one of the **wavelet** computation techniques. Prior DWT architectures are mostly constructed on the basic lifting scheme or the flipping structure. In order to attain a critical path with only one multiplier, at least four pipelining stages are mandatory for one lifting step, or a large temporal buffer is required. In this work, modifications are made in the lifting scheme as the Radix-8 booth multiplier is used and the intermediate values are recombined and stored to reduce the number of pipelining stages and the registers. The two- input/two-output parallel scanning architecture is adopted in the design. The detailed analysis is performed to compare the proposed architecture with the modified architecture in terms of hardware complexity computation time and Power consumption. In the proposed architecture, the number of LUTs reduced to 50%, power consumption is reduced to 89mw, and computation time delay is reduced to 36.6% when compared to the conventional Lifting Scheme.

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Filter Unit is a very important unit in every **Discrete** **Wavelet** **Transform** (DWT) architecture. The rest of the paper is organized as follows. Section two and Section three briefly describes Literature review and **Discrete** **Wavelet** **Transform**. Section four presents Data Dependencies within DWT. Proposed Filter Unit and its Filter cell is described in Section five. Section six presents the Hardware Implementation of Filter Unit. Simulation results are shown in Section seven and conclusions are drawn in Section eight.

ABSTRACT: Conventional distributed arithmetic (DA) is popular in field programmable gate array (FPGA) design, and it features on-chip ROM to achieve high speed and regularity. In this paper, we describe high speed area efficient 1-D **discrete** **wavelet** **transform** (DWT) using 9/7 filter based distributed arithmetic (DA) Technique. Being area efficient architecture free of ROM, multiplication, and subtraction, DA can also expose the redundancy existing in the adder array consisting of entries of 0 and 1. This architecture supports any size of image pixel value and any level of decomposition. The parallel structure has 100% hardware utilization efficiency.

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Abstract- Image Fusion is a technique by which two or more images are combined together to generate a single image that has important properties of both the original images. Generally, multifocal images are combined together with the help of image fusion to generate a high quality image. Other domain where Image fusion is readily used nowadays is in medical diagnostics to fuse medical images such as CT (Computed Tomography), MRI (Magnetic Resonance Imaging) and MRA. This paper aims to present a new algorithm to improve the quality of multimodality medical image fusion using **Discrete** **Wavelet** **Transform** (DWT) approach. **Discrete** **Wavelet** **transform** has been implemented using different fusion techniques including pixel averaging, min-max and max-min methods for medical image fusion. Performance of fusion is calculated on the basis of PSNR, MSE and the total processing time and the results demonstrate the effectiveness of fusion scheme based on **wavelet** **transform**.

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Abstract—The denoising of electrocardiogram (ECG) represents the entry point for the processing of this signal. The widely algorithms for ECG de- noising are based on **discrete** **wavelet** **transform** (DWT). In the other side the performances of denoising process considerably influence the operations that follow. These performances are quantified by some ratios such as the output signal on noise (SNR) and the mean square error (MSE) ratio. This is why the optimal selection of denoising parameters is strongly recommended. The aim of this work is to define the optimal **wavelet** function to use in DWT decomposi- tion for a specific case of ECG denoising. The choice of the appropriate thresh- old method giving the best performances is also presented in this work. Finally the criterion of selection of levels in which the DWT decomposition must be performed is carried on this paper. This study is applied on the electromyography (EMG), baseline drift and power line interference (PLI) noises.

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This paper presents comparative analysis of image retrieval systems based on **discrete** **wavelet** **transform** and complex **wavelet** **transform**. Standard **discrete** **wavelet** **transform** (DWT) is non-redundant. So it is very powerful tool for many non-stationary signal processing applications. First we have decomposed DWT up to two levels. To overcome the disadvantages of Dual-Tree **Discrete** **Wavelet** **Transform** such as shift invariance, poor directional selectivity and loss of phase we implemented Dual- Tree Complex **Wavelet** **Transform**. Texture feature is extracted by applying Grey Level Co-occurrence matrix (GLCM) in each sub-bands of DT-DWT and DT-CWT. Euclidian and Canberra distances are used for similarity measures. Then image retrieval efficiency of DT-DWT and DT-CWT is compared for performance measurement.

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The first step in the analysis of PQ disturbances is their detection and consists of two steps: feature extraction and classification that is performed based on the model shown in Fig.1 (Block diagram of the detection of disturbance system.) This paper presents multi resolution signal decomposition technique as a powerful tool for detecting and classifying disturbances in the electrical distribution system. The proposed technique will deal with the problem not only in time domain or frequency domain, but in a **wavelet** domain which covers both the time and frequency domains. Multi resolution signal decomposition technique can detect and diagnose defects and provide early warning of impending power quality problems. Using the properties of the **wavelet** and the features in the decomposed waveform one will have the ability to extract important information from the distorted signal at different resolution levels and classify the types of disturbance. Here the signals of disturbance waveform has been analysed with **Discrete** **Wavelet** **Transform** (DWT). Fig. 8, 9, 10,11,12,13 and 14 shows the analysis of the signal of sag. Transient, fluctuation, interruption, normal and swell disturbance by **wavelet** Db4. As far as the detection and the localization are concerned the first inner decomposition level of the signal (CD1) is normally adequate to detect and localize any disturbance in the signal.

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This paper proposes the image fusion based on counterlet **transform** and **discrete** **wavelet** **transform**. The DWT and CT **transform** are used to extract the best features from different blur input images. The images are portioned based on dimensional reduction methods such as Laplacian pyramid and different coefficients from **discrete** **wavelet** **transform** to enhance the mean square error (MSE) and peak signal to noise ratio (PSNR) for exhibit the good appearance of output image i.e. image fusion. Hybrid DWT architecture has the advantage of lowers computational complexities and higher efficiencies. The algorithm is written in system MATLAB software. Image fusion based on contoulet **transform** and **discrete** **wavelet** **transform** gives better MSE and PSNR results as compared to existing methods.

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Abstract— in this paper, our system propose to recognize and classify the currency notes by using different steps starting from image acquisition, preprocessing, testing, training. Methodology used for feature extraction is **Discrete** **Wavelet** **Transform** (DWT) and approximate coefficient matrix of the currency image is derived. Statistical features are extracted using coefficient and stored in a vector. Extracted features are used to classify the currency note using Probabilistic Neural Network [1].

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The **discrete** **wavelet** **transform** (DWT) has been extensively studied and developed in various scientific and engineering fields. The multiresolution and local nature of the DWT facilitates applications requiring progressiveness and the capture of high-frequency details. However, the intensive computation of DWT caused by multilevel filtering/down-sampling will become a significant bottleneck in real-time applications when the data size is large. This paper presents a SIMD-based parallel processing framework as a commodity solution to this problem, that is based on the consumer-level programmable graphic processing unit (GPU) on personal computers. Simulation tests show that, in contrast to those CPU-based solutions for DWT, this GPU-based parallel processing framework can bring a significant performance gain on a normal PC without extra cost.

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