Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

Wavelet Transforms and Edge Detection

Abstract: A wavelet transform of a function is, roughly speaking, a description of this function across a range of scales. We use the technique of wavelet transforms to detect discontinuities in the n-th derivative of a function of one variable.

Gabor Transform, SPWVD, Gabor-Wigner Transform and Wavelet Transform - Tools For Power Quality Monitoring

Abstract: The one-dimension frequency analysis based on DFT (Discrete FT ) is sufficient in many cases in detecting power disturbances and evaluating power quality (PQ). To illustrate in a more comprehensive manner the character of the signal, time-frequency analyses are p erformed. The most common known time-frequency representations (TFR) are spectrogram (SPEC) and Gabor Transform (GT). However, the method has a relatively low time-frequency resolution. The other TF R: Discreet Dyadic Wavelet Transform (DDWT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and new Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, are presented.

Enhanced method for reducing ultrasound speckle noise using wavelet transform

Abstract: Signal-dependent noise in a coherent imaging system signal, such as in medical ultrasound imaging, is reduced by filtering speckle noise using nonlinear adaptive thresholding of received echo wavelet transform coefficients, thereby enhancing the resultant image by improving the signal-to-noise ratio. The method includes the steps of dividing the imaging system signal into a number of subinterval signals of equal length; transforming each subinterval signal using discrete wavelet transformation to provide wavelet transform coefficients for each of a plurality of wavelet scales having different levels of resolution ranging from a finest wavelet scale to a coarsest wavelet scale: deleting all of the wavelet transform coefficients representing the finest wavelet scale: for each wavelet scale other than the finest wavelet scale, identifying for each subinterval signal which of the wavelet transform coefficients are related to noise and which are related to a true signal through the use of adaptive nonlinear thresholding; selecting those wavelet transform coefficients which are identified as being related to a true signal; and setting to zero those wavelet coefficients which are identified as being related to noise: inverse transforming the modified wavelet transform coefficients using an inverse discrete wavelet transformation to provide an enhanced true signal with reduced noise.

Signal and Image Denoising Using Wavelet Transform

Abstract: The wavelet transform (WT) a powerful tool of signal and image processing that have been successfully used in many scientific fields such as signal processing, image compression, computer graphics, and pattern recognition (Daubechies 1990; Lewis and Knowles 1992; Do and Vetterli 2002; Meyer, Averbuch et al. 2002; Heric and Zazula 2007). On contrary the traditional Fourier Transform, the WT is particularly suitable for the applications of nonstationary signals which may instantaneous vary in time (Daubechies 1990; Mallat and Zhang 1993; Akay and Mello 1998). It is crucial to analyze the time-frequency characteristics of the signals which classified as non-stationary or transient signals in order to understand the exact features of such signals (Rioul and Vetterli 1991; Ergen, Tatar et al. 2010). For this reason, firstly, researchers has concentrated on continuous wavelet transform (CWT) that gives more reliable and detailed time-scale representation rather than the classical short time Fourier transform (STFT) giving a time-frequency representation (Jiang 1998; Qian and Chen 1999).

Fast linear canonical transforms

Abstract: The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.