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A fractional Gabor expansion

We present a fractional Gabor expansion on a non-rectangular time–frequency lattice. Sinusoidal analysis used in the traditional Gabor expansion is not appropriate for a compact representation for chirp-type signals. Basis functions of the proposed expansion are obtained via fractional Fourier basis. Completeness and biorthogonality conditions of the new expansion are derived.

A fractional Gabor transform

We present a fractional Gabor expansion on a general, non-rectangular time-frequency lattice. The traditional Gabor expansion represents a signal in terms of time- and frequency-shifted basis functions, called Gabor logons. This constant-bandwidth analysis results in a fixed, rectangular time frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-frequency lattice for a compact representation. The proposed fractional Gabor expansion uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. The completeness and bi-orthogonality conditions of the new Gabor basis are discussed.

A robust image watermarking in the joint time-frequency domain

With the rapid development of computers and internet applications, copyright protection of multimedia data has become an important problem. Watermarking techniques are proposed as a solution to copyright protection of digital media files. In this paper, a new, robust, and high-capacity watermarking method that is based on spatiofrequency (SF) representation is presented. We use the discrete evolutionary transform (DET) calculated by the Gabor expansion to represent an image in the joint SF domain. The watermark is embedded onto selected coefficients in the joint SF domain. Hence, by combining the advantages of spatial and spectral domain watermarking methods, a robust, invisible, secure, and high-capacity watermarking method is presented. A correlation-based detector is also proposed to detect and extract any possible watermarks on an image. The proposed watermarking method was tested on some commonly used test images under different signal processing attacks like additive noise, Wiener and Median filtering, JPEG compression, rotation, and cropping. Simulation results show that our method is robust against all of the attacks.

Discrete evolutionary transform based robust image watermarking

Watermarking techniques are used as a solution to copyright protection of digital media files. In this work, a new and robust watermarking method that is based on spatio-frequency (SF) representations is presented. We use the discrete evolutionary transform calculated by the Gabor expansion to represent an image in the SF domain. A watermark is embedded onto selected cells in the joint SF domain. Hence by combining the advantages of spatial and spectral domain watermarking methods, a robust and perceptual method is presented.

Interference suppression in DSSS communication systems using instantaneous frequency estimation

In this paper, we consider broadband jammer suppression in direct sequence spread spectrum (DSSS) communication systems. The transmitted signal in DSSS systems occupies a bandwidth much wider than the bandwidth necessary to send the information. Hence these systems are inherently immune to outside interferences or jammers. The performance of DSSS systems can be further improved in terms of immunity to interferences by suppressing the interference prior to despreading and demodulation. Here, we use a time-varying filter that adapts to the instantaneous frequency of the interference signal to suppress broadband jammers in DSSS systems. The IF of the received signal is estimated from an evolutionary spectrum. The performance of our IF estimation and jammer suppression algorithms are presented by means of examples.

A Robust Image Watermarking Based on Time-Frequency

Watermarking techniques are proposed as a solution to copyright protection of digital media files. In this work, a new and robust watermarking method that is based on time-frequency (TF) representations is presented. We use the discrete evolutionary transform to represent an image in the TF domain. A watermark is embedded onto selected cells in the joint TF domain. Hence by combining the advantages of spatial and spectral domain watermarking methods, a robust and perceptual watermarking algorithm is presented.

High capacity image watermarking in the joint spatio-frequency domain

Watermarking techniques are proposed as a solution to copyright protection of digital media files. Watermarking algorithms are mainly concentrated on spatial or spectral domains. In this work, a robust and high capacity watermarking method that is based on spatio-frequency (SF) representations is presented. We use the discrete evolutionary transform (DET) calculated by Gabor expansion to represent an image in the SF domain. A watermark is embedded onto selected coefficients in the joint SF domain. Hence by combining the advantages of spatial and spectral domain watermarking methods, a robust, invisible, secure and high capacity watermarking method is presented.

A multi-window fractional evolutionary spectral analysis

In this work, we present a multiple window evolutionary spectral analysis on a non-rectangular time-frequency lattice based on a discrete fractional Gabor expansion. The traditional Gabor expansion uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals such as speech, music, etc., require a more flexible, nonrectangular time-frequency lattice for a compact representation. The proposed method uses a set of basis functions that are related to the fractional Fourier basis and generates a parallelogram-shaped tiling. Simulation results are given to illustrate the performance of our algorithm.