Showing papers on "Harmonic wavelet transform published in 2008"
01 Jan 2008
TL;DR: This book presents an introduction to the principles of the fast Fourier transform, which covers FFTs, frequency domain filtering, and applications to video and audio signal processing.
Abstract: This manuscript describes a number of algorithms that can be used to quickly evaluate a polynomial over a collection of points and interpolate these evaluations back into a polynomial. Engineers define the “Fast Fourier Transform” as a method of solving the interpolation problem where the coefficient ring used to construct the polynomials has a special multiplicative structure. Mathematicians define the “Fast Fourier Transform” as a method of solving the evaluation problem. One purpose of the document is to provide a mathematical treatment of the topic of the “Fast Fourier Transform” that can also be understood by someone who has an understanding of the topic from the engineering perspective.
The manuscript will also introduce several new algorithms that solve the fast multipoint evaluation problem over certain finite fields and require fewer finite field operations than existing techniques. The document will also demonstrate that these new algorithms can be used to multiply polynomials with finite field coefficients with fewer operations than Schonhage's algorithm in most circumstances.
A third objective of this document is to provide a mathematical perspective of several algorithms which can be used to multiply polynomials of size which is not a power of two. Several improvements to these algorithms will also be discussed.
Finally, the document will describe several applications of the “Fast Fourier Transform” algorithms presented and will introduce improvements in several of these applications. In addition to polynomial multiplication, the applications of polynomial division with remainder, the greatest common divisor, decoding of Reed-Solomon error-correcting codes, and the computation of the coefficients of a discrete Fourier Series will be addressed.
272 citations
01 Jan 2008
TL;DR: In the first step an attempt was made to generate ECG wave- forms by developing a suitable MATLAB simulator and in the second step, using wavelet transform, the ECG signal was denoised by removing the corresponding wavelet coefficients at higher scales.
Abstract: This paper deals with the study of ECG signals using wavelet trans- form analysis. In the first step an attempt was made to generate ECG wave- forms by developing a suitable MATLAB simulator and in the second step, using wavelet transform, the ECG signal was denoised by removing the corresponding wavelet coefficients at higher scales. Then QRS complexes were detected and each complex was used to find the peaks of the individual waves like P and T, and also their deviations.
214 citations
TL;DR: This paper compares and contrasts this transform with the better known continuous wavelet transform, and defines a relation between both that allows a better understanding of the S-transform.
Abstract: The S-transform is becoming popular for time-frequency analysis and data-adaptive filtering thanks to its simplicity. While this transform works well in the continuous domain, its discrete version may fail to achieve accurate results. This paper compares and contrasts this transform with the better known continuous wavelet transform, and defines a relation between both. This connection allows a better understanding of the S-transform, and makes it possible to employ the wavelet reconstruction formula as a new inverse S-transform and to propose several methods to solve some of the main limitations of the discrete S-transform, such as its restriction to linear frequency sampling.
159 citations
TL;DR: The algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fouriertransform, both in terms of speed and accuracy.
Abstract: We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ~ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.
154 citations
TL;DR: A DWT technique which is combined with a feature selection of energy spectrum and fault classification using neural network for analyzing fault signal is proposed for improving the shortcomings without losing its original property.
Abstract: An investigation of a fault diagnostic technique for internal combustion engines using discrete wavelet transform (DWT) and neural network is presented in this paper. Generally, sound emission signal serves as a promising alternative to the condition monitoring and fault diagnosis in rotating machinery when the vibration signal is not available. Most of the conventional fault diagnosis techniques using sound emission and vibration signals are based on analyzing the signal amplitude in the time or frequency domain. Meanwhile, the continuous wavelet transform (CWT) technique was developed for obtaining both time-domain and frequency-domain information. Unfortunately, the CWT technique is often operated over a longer computing time. In the present study, a DWT technique which is combined with a feature selection of energy spectrum and fault classification using neural network for analyzing fault signal is proposed for improving the shortcomings without losing its original property. The features of the sound emission signal at different resolution levels are extracted by multi-resolution analysis and Parseval's theorem [Gaing, Z. L. (2004). Wavelet-based neural network for power disturbance recognition and classification. IEEE Transactions on Power Delivery 19, 1560-1568]. The algorithm is obtained from previous work by Daubechies [Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Communication on Pure and Applied Mathematics 41, 909-996.], the''db4'', ''db8'' and ''db20'' wavelet functions are adopted to perform the proposed DWT technique. Then, these features are used for fault recognition using a neural network. The experimental results indicated that the proposed system using the sound emission signal is effective and can be used for fault diagnosis of various engine operating conditions.
147 citations
TL;DR: In this paper, a new viewpoint in ECG detection is presented using continuous wavelet transform (CWT), and the concept of dominant rescaled wavelet coefficients (DRWC) is defined to magnify QRS complex and reduce the effects of other peaks.
143 citations
TL;DR: In this work, four uncertainty relations between LCT pairs are presented and their implications in some common optical systems are discussed.
Abstract: The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this work we present four uncertainty relations between LCT pairs and discuss their implications in some common optical systems.
138 citations
01 Jan 2008
TL;DR: In this paper, the FFT Algorithm with Radix-2 Decimation-in-Frequency (DIF) algorithm is presented, which is based on the Radix 2 Bit Reversal algorithm.
Abstract: This chapter contains sections titled: Introduction Development of the FFT Algorithm with Radix-2 Decimation-in-Frequency FFT Algorithm with Radix-2 Decimation-in-Time FFT Algorithm with Radix-2 Bit Reversal for Unscrambling Development of the FFT Algorithm with Radix-4 Inverse Fast Fourier Transform Programming Examples References
124 citations
TL;DR: The basis selection algorithm by Coifman and Wickerhauser is adapted, providing a solution to the basis selection problem for the DWPT, and it is shown how to extend the two-band to an -band using the same method.
Abstract: The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo for a given signal. The discrete wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal at hand. However, it is well known that both the DWT and the DWPT are shift-varying. Also, when these transforms are extended to 2-D and higher dimensions using tensor products, they do not provide a geometrically oriented analysis. The dual-tree complex wavelet transform , introduced by Kingsbury, is approximately shift-invariant and provides directional analysis in 2-D and higher dimensions. In this paper, we propose a method to implement a dual-tree complex wavelet packet transform , extending the as the DWPT extends the DWT. To find the best complex wavelet packet frame for a given signal, we adapt the basis selection algorithm by Coifman and Wickerhauser, providing a solution to the basis selection problem for the . Lastly, we show how to extend the two-band to an -band (provided that ) using the same method.
116 citations
01 Jan 2008
TL;DR: This paper proposes to investigate the suitability of different wavelet bases and the size of different neighborhood on the performance of image de-noising algorithms in terms of PSNR, and the impact of wavelet coefficients arising from the standard discrete wavelet transform.
Abstract: Summary The image de-noising naturally corrupted by noise is a classical problem in the field of signal or image processing. Additive random noise can easily be removed using simple threshold methods. De-noising of natural images corrupted by Gaussian noise using wavelet techniques are very effective because of its ability to capture the energy of a signal in few energy transform values. The wavelet de-noising scheme thresholds the wavelet coefficients arising from the standard discrete wavelet transform. In this paper, it is proposed to investigate the suitability of different wavelet bases and the size of different neighborhood on the performance of image de-noising algorithms in terms of PSNR.
110 citations
TL;DR: These transforms provide enough features of the PCG signals that will help clinics to obtain qualitative and quantitative measurements of the time-frequency (TF) PCG signal characteristics and consequently aid diagnosis.
TL;DR: A novel image encryption algorithm is proposed based on the multiple-parameter fractions of Fourier transform, which is a generalized fractional Fouriertransform, without the use of phase keys, and shows superior robustness to blind decryption.
Abstract: A novel image encryption algorithm is proposed based on the multiple-parameter fractional Fourier transform, which is a generalized fractional Fourier transform, without the use of phase keys. The image is encrypted simply by performing a multiple-parameter fractional Fourier transform with four keys. Optical implementation is suggested. The method has been compared with existing methods and shows superior robustness to blind decryption.
TL;DR: In this paper, a new perspective for the IEEE standard 1459-2000 definitions is introduced using the stationary wavelet transform (SWT), which can provide variable frequency resolution while preserving time information without spectral leakage as the FFT.
Abstract: Power components, power factors, and pollution factor are defined according to the IEEE standard 1459-2000 based on the fast Fourier transform (FFT). However, the FFT in the presence of nonstationary power quality (PQ) disturbances results in inaccurate values due to its sensitivity to the spectral leakage problem. In this paper, a new perspective for the IEEE standard 1459-2000 definitions is introduced using the stationary wavelet transform (SWT). As a time-frequency transform, the SWT can provide variable frequency resolution while preserving time information without spectral leakage as the FFT. Moreover, unlike other time-frequency transforms, such as discrete wavelet transform (DWT), SWT possesses the time-invariance property that keeps the time and frequency characteristics throughout all of the decomposition levels. Results of different case studies including stationary, nonstationary of synthetic, and real PQ disturbances proves the effectiveness of applying the SWT over FFT or DWT.
TL;DR: This paper introduces a transform that is called the biquaternion Fourier transform (BiQFT), and shows how it can be used to generalize the notion of analytic signal to complex-valued signals.
Abstract: In this paper, we consider the extension of the Fourier transform to biquaternion-valued signals. We introduce a transform that we call the biquaternion Fourier transform (BiQFT). After giving some general properties of this transform, we show how it can be used to generalize the notion of analytic signal to complex-valued signals. We introduce the notion of hyperanalytic signal. We also study the Hermitian symmetries of the BiQFT and their relation to the geometric nature of a biquaternion-valued signal. Finally, we present a fast algorithm for the computation of the BiQFT. This algorithm is based on a (complex) change of basis and four standard complex FFTs.
TL;DR: In this article, wavelet transform (discrete wavelet and wavelet packet transform) was introduced into a fourth-order statistic, kurtosis, for fault diagnosis in rolling element bearings.
Abstract: Signal processing plays a pivotal role in fault diagnostics of mechanical systems. An approach, viz. wavelet transform-based higher-order statistics, was developed in this paper for fault diagnosis in rolling element bearings. In the approach, wavelet transform (discrete wavelet and wavelet packet transform) was introduced into a fourth-order statistic, kurtosis. Thereinto, discrete wavelet transform-based kurtosis (DWTK) was applied to signals to get a higher resolution in low-frequency bands1 on the other hand, wavelet packet transform-based kurtosis (WPTK) was applied to obtain a relatively high resolution in high-frequency bands in comparison with the DWTK. DWTK, WPTK and wavelet transform-based kurtosis (WTK) curves were introduced to calibrate the in-field signals in comparison with the benchmark signals, whereby the non-stationary transients and singularity in the vibration signals attributed to damage were detected. WTK curves of vibration signals collected from bearing with damage of different se...
01 Dec 2008
TL;DR: The recognition rates of the method proposed outperform remarkably those of the classic PCA or KPCA especially when combining block-based and multi-resolution methods.
Abstract: This paper proposes a novel method based on Haar wavelet transform and uniform local binary patterns (ULBPs) to recognize ear images. Firstly, ear images are decomposed by Haar wavelet transform. Then ULBPs are combined simultaneously with block-based and multi-resolution methods to describe together the texture features of ear sub-images transformed by Haar wavelet. Finally, the texture features are classified by the nearest neighbor method. Experimental results show that Haar wavelet transform can boost effectively up intensity information of texture unit. It is not only fast but also robust to use ULBPs to extract texture features. The recognition rates of the method proposed by this paper outperform remarkably those of the classic PCA or KPCA especially when combining block-based and multi-resolution methods.
TL;DR: In this article, the advantages of adaptive Fourier transform and analytical wavelet transform as compared to traditional Fourier Transform have been discussed, which make it possible to reliably detect wave-like disturbances against a background of noise at a signal-to-noise ratio not less than 0.1.
Abstract: Backgrounds of adaptive Fourier transform and analytical wavelet transform have been briefly described in comparison with traditional Fourier transform using a time window. As an example, all three transforms are used to analyze quasiperiodic wave-like processes in the ionosphere, which accompanied the passage of the solar terminator and rocket launch from the Plesetsk site. The advantages of adaptive Fourier transform and analytical wavelet transform as compared to traditional Fourier transform, which make it possible to reliably detect wave-like disturbances against a background of noise at a signal-to-noise ratio not less than 0.1, have been demonstrated.
TL;DR: The use of wavelet transform in multicarrier ultra wideband (UWB) systems is analysed and the results are compared with Fourier-based multicarriers UWB systems and a performance comparison of both techniques for IEEE 802.15.3a channel models is provided.
Abstract: The use of wavelet transform in multicarrier ultra wideband (UWB) systems is analysed and the results are compared with Fourier-based multicarrier UWB systems. It is well known that convolution in time domain is equivalent to multiplication in frequency domain; however, there is no closed-form expression in the literature for convolution's counterpart in the wavelet domain. A formula is derived to represent convolution's counterpart in the wavelet domain. Furthermore, the effects of choice and type of wavelet filters and different decomposition levels are investigated. Finally, a performance comparison of both techniques for IEEE 802.15.3a channel models using IEEE802.15.3a multiband-orthogonal frequency division multiplexing UWB specifications is provided.
TL;DR: A novel method is presented where encrypted covert data is embedded into the coefficients of the host audio (cover signal) in the integer wavelet domain where the hearing threshold is calculated and this threshold is employed as the embedding threshold.
Abstract: In this paper a novel method for digital audio steganography is presented where encrypted covert data is embedded into the coefficients of the host audio (cover signal) in the integer wavelet domain. The hearing threshold is calculated in the integer domain and this threshold is employed as the embedding threshold. The inverse integer wavelet transform is applied to the modified coefficients to form a new audio sequence (stego signal). The characteristics of this method are large payload, high audio quality and full recovery.
TL;DR: A new method called fractional wavelet packet transform to encrypt images in this paper, in which fractional orders andWavelet packet filter are its two series of keys.
14 Oct 2008
TL;DR: This abstract introduces the fast S-transform, a more efficient discrete implementation of the classic S- transform with dramatically reduced computational requirements.
Abstract: Determining the frequency content of a signal is a basic operation in signal and image processing. The S-transform provides both the true frequency and globally referenced phase measurements characteristic of the Fourier transform and also generates local spectra, as does the wavelet transform. Due to this combination, the S-transform has been successfully demonstrated in a variety of biomedical signal and image processing tasks. However, the computational demands of the S-transform have limited its application in medicine to this point in time. This abstract introduces the fast S-transform, a more efficient discrete implementation of the classic S-transform with dramatically reduced computational requirements.
TL;DR: The characteristics of the classic and short time Fourier transform are compared with the continuous wavelet transform to better understand the generation and propagation of conducted noise from the noise source, the switching devices, to the point where the noise is actually measured, the line impedance stabilization network.
Abstract: This paper compares the characteristics of the classic and short time Fourier transform with the continuous wavelet transform. The wavelet transform perfectly suits the considered application, the study of the time evolution of frequency spectra in switched mode power supplies, which operate with significant transients. The analysis made with wavelets offers a means to better understand the generation and propagation of conducted noise from the noise source, the switching devices, to the point where the noise is actually measured, the line impedance stabilization network.
TL;DR: The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm, and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function.
Abstract: Contactless conductivity detector technology has unique advantages for microfluidic applications. However, the low S/N and varying baseline makes the signal analysis difficult. In this paper, a continuous wavelet transform-based peak detection algorithm was developed for CE signals from microfluidic chips. The Ridger peak detection algorithm is based on the MassSpecWavelet algorithm by Du et al. [Bioinformatics 2006, 22, 2059-2065], and performs a continuous wavelet transform on data, using a wavelet proportional to the first derivative of a Gaussian function. It forms sequences of local maxima and minima in the continuous wavelet transform, before pairing sequences of maxima to minima to define peaks. The peak detection algorithm was tested against the Cromwell, MassSpecWavelet, and Linear Matrix-assisted laser desorption/ionization-time-of-flight-mass spectrometer Peak Indication and Classification algorithms using experimental data. Its sensitivity to false discovery rate curve is superior to other techniques tested.
01 Jan 2008
TL;DR: In this article, the authors proposed a multiresolution analysis that reexpresses a time series as the sum of several new series, each of which is associated with a particular scale.
Abstract: Discrete wavelet transforms (DWTs) are mathematical tools that are useful for analyzing geophysical time series The basic idea is to transform a time series into coefficients describing how the series varies over particular scales One version of the DWT is the maximal overlap DWT (MODWT) The MODWT leads to two basic decompositions The first is a scale-based analysis of variance known as the wavelet variance, and the second is a multiresolution analysis that reexpresses a time series as the sum of several new series, each of which is associated with a particular scale Both decompositions are illustrated through examples involving Arctic sea ice and an Antarctic ice core A second version of the DWT is the orthonormal DWT (ODWT), which can be extracted from the MODWT by subsampling The relative strengths and weaknesses of the MODWT, the ODWT and the continuous wavelet transform are discussed
TL;DR: In analyzing the SP and GR logs from a field, both the wavelet transform method and conventional well log analysis showed similar results, however, the results from a combination of theWavelet transform and the Fourier transform methods were better than those from the wavelets method and the conventionalWell log analysis.
12 Dec 2008
TL;DR: A novel codec of depth-image-based representations for free-viewpoint 3D-TV relies on a shape-adaptive wavelet transform and an explicit representation of the locations of major depth edges, which greatly reduces the data entropy.
Abstract: We present a novel codec of depth-image-based representations for free-viewpoint 3D-TV. The proposed codec relies on a shape-adaptive wavelet transform and an explicit representation of the locations of major depth edges. Unlike classical wavelet transforms, the shape-adaptive transform generates small wavelet coefficients along depth edges, which greatly reduces the data entropy. The codec also shares the edge information between the depth map and the image to reduce their correlation. The wavelet transform is implemented by shape-adaptive lifting, which enables fast computations and perfect reconstruction. Experimental results on real data confirm the superiority of the proposed codec, with PSNR gains of up to 5.46 dB on the depth map and up to 0.19 dB on the image compared to standard wavelet codecs.
TL;DR: In this paper, a wavelet-based model of local stationarity is introduced, which enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time.
Abstract: We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on scales. We propose a pointwise adaptive estimator of the time-varying spectrum. The behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum.
TL;DR: This research adopts the wavelet transform in the analysis of impact echo data to avoid ripple and multiple-peak phenomena and combines the Fourier spectrum and wavelet marginal spectrum to determine the precise location of the echo peak.
Abstract: The objective of this study is to develop a reliable and effective method to analyze the signal of the impact echo test. The impact echo test is a nondestructive testing technique for civil structures. In the test, the surface response of the target structure due to an impact is measured. Then, the Fourier transform is adopted to transform the signal from the time domain to the frequency domain. Owing to the multiple reflections induced by cracks, voids, or other interfaces, peaks will form in the Fourier spectrum. The frequencies of the peaks can then be used to determine the size of the structure or the location of the defect. Several difficulties are encountered when applying the Fourier transform to impact echo data. Because the impact echo data are non-stationary and contains multiple reflections, ripples and multiple peaks appear in the Fourier spectrum, which may mislead the follow-up diagnosis. Furthermore, the existence of the high-energy surface wave and structural vibrations often complicates the spectrum and makes the data interpretation even more difficult. To overcome these difficulties, this research adopts the wavelet transform in the analysis of impact echo data. Theoretically, the wavelet transform can avoid ripple and multiple-peak phenomena. Furthermore, the frequency range and time span of surface wave can be observed in the wavelet scalogram. However, the spectral resolution of the wavelet marginal spectrum is inferior to that of the Fourier transform. Therefore, two approaches are proposed in this paper. One is to combine the Fourier spectrum and the wavelet marginal spectrum to determine the precise location of the echo peak. The other is to take the product of the two spectra to establish the enhanced Fourier spectrum. As such, the interference in the Fourier spectrum is suppressed while the peak is enhanced. Numerical and experimental tests were performed to verify the effectiveness and reliability of the proposed approaches.
TL;DR: In this paper, the authors extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces, and obtain equivalent norms on Bochner spaces in terms of g-functions.
Abstract: We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.
TL;DR: The experimental results show that the proposed algorithm improves the recognition rate about 12 percents and compared the proposed scheme with two well-known rotation invariant methods; Fourier-wavelet and Zernike moments.