Signal quantitative analysis using customizable perfect-translation-invariant complex wavelet functions

2014 ◽  
Vol 12 (04) ◽  
pp. 1460010 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang
Keyword(s):  
Quantitative Analysis ◽  
Frequency Band ◽  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Digital Signals ◽  
Orthonormal Wavelet ◽  
Translation Invariant ◽  
Fast Calculation ◽  
Complex Wavelet

In this paper, we introduce several methods of signal quantitative analysis using the perfect-translation-invariant complex wavelet functions (PTI complex wavelet functions), which are used in our proposed perfect-translation-invariant complex discrete wavelet transforms (PTI CDWTs) and can be designed by customization. First, using PTI complex wavelet functions, we define the continuous wavelet coefficient (CWC). Next, using orthonormal wavelet functions in the classical Hardy space, we analyze the CWC, and show that, using a CWC, we can measure the energy of a customizable frequency band, and additionally, using numbers of CWCs, we can measure the energy of the whole frequency band. Next, we introduce the fast calculation method of CWCs and show the applicability of the PTI CDWTs to digital signals. Based on them, we introduce some examples of signal quantitative analysis, including the methods to obtain instantaneous amplitude, instantaneous phase and instantaneous frequency. Additionally, we introduce the energy measurement of the whole frequency band using the PTI DT-CDWT, which is one of our proposed PTI CDWTs.

Perfect-translation-invariant variable-density complex discrete wavelet transform

2014 ◽  
Vol 12 (04) ◽  
pp. 1460001 ◽  
Author(s):  
Hiroshi Toda ◽  
Zhong Zhang ◽  
Takashi Imamura
Keyword(s):  
Frequency Domain ◽  
Frequency Band ◽  
Time Domain ◽  
Wavelet Transforms ◽  
Filter Banks ◽  
Wavelet Packet ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Logarithmic Scale ◽  
The Time Domain

The theorems giving the conditions for discrete wavelet transforms (DWTs) to achieve perfect translation invariance (PTI) have already been proven, and based on these theorems, the dual-tree complex DWT and the complex wavelet packet transform, achieving PTI, have already been proposed. However, there is not so much flexibility in their wavelet density. In the frequency domain, the wavelet density is fixed by octave filter banks, and in the time domain, each wavelet is arrayed on a fixed coordinate, and the wavelet packet density in the frequency domain can be only designed by dividing an octave frequency band equally in linear scale, and its density in the time domain is constrained by the division number of an octave frequency band. In this paper, a novel complex DWT is proposed to create variable wavelet density in the frequency and time domains, that is, an octave frequency band can be divided into N filter banks in logarithmic scale, where N is an integer larger than or equal to 3, and in the time domain, a distance between wavelets can be varied in each level, and its transform achieves PTI.

scholarly journals Two-Layer Fragile Watermarking Method Secured with Chaotic Map for Authentication of Digital Holy Quran

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
Mohammed S. Khalil ◽  
Fajri Kurniawan ◽  
Muhammad Khurram Khan ◽  
Yasser M. Alginahi
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Coefficient ◽  
Chaotic Map ◽  
Spatial Domain ◽  
Fragile Watermarking ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Wavelet Domain ◽  
Good Image Quality ◽  
Holy Quran

This paper presents a novel watermarking method to facilitate the authentication and detection of the image forgery on the Quran images. Two layers of embedding scheme on wavelet and spatial domain are introduced to enhance the sensitivity of fragile watermarking and defend the attacks. Discrete wavelet transforms are applied to decompose the host image into wavelet prior to embedding the watermark in the wavelet domain. The watermarked wavelet coefficient is inverted back to spatial domain then the least significant bits is utilized to hide another watermark. A chaotic map is utilized to blur the watermark to make it secure against the local attack. The proposed method allows high watermark payloads, while preserving good image quality. Experiment results confirm that the proposed methods are fragile and have superior tampering detection even though the tampered area is very small.

A NOVEL DESIGN METHOD FOR DIRECTIONAL SELECTION BASED ON 2-DIMENSIONAL COMPLEX WAVELET PACKET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360010 ◽  
Author(s):  
TAKESHI KATO ◽  
ZHONG ZHANG ◽  
HIROSHI TODA ◽  
TAKASHI IMAMURA ◽  
TETSUO MIYAKE
Keyword(s):  
Wavelet Transforms ◽  
Design Method ◽  
Wavelet Packet ◽  
Wavelet Packet Transform ◽  
Directional Selection ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Semiconductor Wafer ◽  
Directional Filters ◽  
Complex Wavelet

In this paper, we propose a design method for directional selection in the two-dimensional complex wavelet packet transform (2D-CWPT). Current two-dimensional complex discrete wavelet transforms (2D-CDWT) can extract directional components from images, but the number of directions is small, and the directions and resolutions are fixed. Thus the current 2D-CDWTs are not flexible enough. In this study, we propose a new design method of the directional filters that can detect desirable direction components. Additionally flexible directional selection is achieved because the directional filters are added to the 2D-CWPT. Finally, the proposed method is applied to defect detection in semiconductor wafer circuits and an encouraging result is obtained.

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

The Morlet and Daubechies Wavelet Transforms for Fatigue Strain Signal Analysis

2013 ◽  
Vol 471 ◽  
pp. 197-202 ◽  
Author(s):  
T.E. Putra ◽  
S. Abdullah ◽  
Mohd Zaki Nuawi ◽  
Mohd Faridz Mod Yunoh
Keyword(s):  
Wavelet Transforms ◽  
Signal Analysis ◽  
Wavelet Coefficient ◽  
Discrete Wavelet ◽  
Daubechies Wavelet ◽  
Wavelet Coefficients ◽  
Public Road ◽  
Road Surfaces ◽  
Strain Signal ◽  
Wavelet Family

This paper presents the convenient wavelet family for the fatigue strain signal analysis based on the wavelet coefficients. This study involves the Morlet and Daubechies wavelet coefficients using both the Continuous and Discrete Wavelet Transforms, respectively. The signals were collected from a front lower suspension arm of a passenger car by placing strain gauges at the highest stress locations. The car was driven over public road surfaces, i. e. pavé, highway and UKM roads. In conclusion, the Daubechies wavelet was the convenient wavelet family for the analysis. It was because the wavelet gave the higher wavelet coefficient values indicating that the resemblance between the wavelet and the signals was stronger, closer and more similar.

THE DESIGN OF COMPLEX WAVELET PACKET TRANSFORMS BASED ON PERFECT TRANSLATION INVARIANCE THEOREMS

2010 ◽  
Vol 08 (04) ◽  
pp. 537-558 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Wavelet Packets ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Discrete Wavelet Transforms ◽  
Wide Range ◽  
Different Shapes ◽  
Complex Wavelet ◽  
Meyer Wavelet

The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

scholarly journals Perbandingan Real-Valued dan Complex Wavelet Transform pada Denoising Sinyal Fetal-Phonocardiograms (Comparison of Fetal-Phonocardiogram Signal Denoising based on Real- Valued and Complex Wavelet Transform)

2020 ◽  
Vol 9 (1) ◽  
pp. 63-72
Author(s):  
Dodi Zulherman ◽  
Jans Hendry ◽  
Ipam Fuadina Adam
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Signal To Noise Ratio ◽  
Well Being ◽  
Discrete Wavelet ◽  
Interference Signal ◽  
Complex Wavelet Transform ◽  
Invasive Method ◽  
Complex Wavelet ◽  
Acoustic Recording

Monitoring of Fetal Heart Rate (FHR) in the pregnancy period commonly uses the Doppler-based instruments despite having several disadvantages, such as high-cost and complexity of the monitoring system. Implementation of the passive and non-invasive method based on fetal phonocardiogram (fPCG), the acoustic recording of fetus cardiac signal, can be used as a potentially economical long-term monitoring device for diagnosis. Because the interference signal from the maternal women exists, the matured denoising technique was needed to implement the fPCG method to diagnose the fetus' well-being condition. The denoising system based on Dual-tree Complex Wavelet Transforms (DTCWT) was proposed in this paper. The proposed method was evaluated using Signal to Noise Ratio (SNR). Based on the experiment result from 37 fPCG signals from physio.net, the DTCWT system performance was compared with the Discrete Wavelet Transform (DWT). There were 24 CWT’s denoised fPCG signals that have successfully outperformed DWT’s SNR. DTCWT has also reduced the noises in the range of 30 Hz–80 Hz. Also, it emphasized the existence of dominant frequencies in the range of 60 Hz–65 Hz.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

Sign in / Sign up

Export Citation Format

Share Document