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.

Automatic Earthquake Signal Onset Picking Based on the Continuous Wavelet Transform

Abstract: This paper presents a method for automatic earthquake signal phase picking based on the continuous wavelet transform (CWT) of the seismogram, namely, the wavelet phase picker (WPP) A characteristic function is defined using the envelope function of CWT coefficients of the vertical component seismogram The performance of the WPP method is evaluated on a database consisting of more than 460 local seismograms, and the P-phases detected by the algorithm are compared with those reported in the database This evaluation confirms the high accuracy of automatically detected picks for the majority of seismograms In addition, the results obtained by the algorithm are compared with a well-known method of P-phase picking referred to as the autoregressive Akaike information criteria This comparison demonstrates the reliability of the proposed method

Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications

Abstract: Least-squares spectral analysis, an alternative to the classical Fourier transform, is a method of analyzing unequally spaced and non-stationary time series in their first and second statistical moments. However, when a time series has components with low or high amplitude and frequency variability over time, it is not appropriate to use either the least-squares spectral analysis or Fourier transform. On the other hand, the classical short-time Fourier transform and the continuous wavelet transform do not consider the covariance matrix associated with a time series nor do they consider trends or datum shifts. Moreover, they are not defined for unequally spaced time series. A new method of analyzing time series, namely, the least-squares wavelet analysis is introduced, which is a natural extension of the least-squares spectral analysis. This method decomposes a time series to the time–frequency domain and obtains its spectrogram. In addition, the probability distribution function of the spectrogram is derived that identifies statistically significant peaks. The least-squares wavelet analysis can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability, including datum shifts, trends, and constituents of known forms, by taking into account the covariance matrix associated with the time series. The outstanding performance of the proposed method on synthetic time series and a very long baseline interferometry series is demonstrated, and the results are compared with the weighted wavelet Z-transform.

Optical encryption using a localized fractional Fourier transform

Abstract: We propose a new method to encrypt and decrypt a two-dimensional amplitude image, which uses a jigsaw transform and a localized fractional Fourier transform. The jigsaw transform is applied to the original image to be encrypted, and the image is then divided into independent nonoverlapping segments. Each image segment is encrypted using different fractional parameters and two statistically independent random phase codes. The random phase codes, along with the set of fractional orders and jigsaw transform index, form the key to the encrypted data. Results of computer simulation are presented to verify the proposed idea and analyze the performance of the method. We also propose an optical implementation, which may find application for encrypting data stored in holographic memory.

Randomization of the Fourier transform

Abstract: We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.

Robust watermarking using fractional wavelet packet transform

Abstract: In this study, the concept of fractional wavelet packet transform is explored with its application in digital watermarking. The core idea of the proposed watermarking scheme is to decompose an image via fractional wavelet packet transform and then a reference image is created by changing the positions of all frequency sub-bands at each level with respect to some rule which is secret and only known to the owner/creator. For embedding, the reference image is segmented into non-overlapping blocks and modify its singular values with the watermark singular values. Finally, a reliable watermark extraction algorithm is developed for the extraction of watermark from the distorted image. The feasibility of this method and its robustness against different kind of attacks are verified by computer simulations.