A matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be correlated with the received signal which can be carried out by multiplication in the frequency domain by applying Fourier Transform (FT). Fracti...

In this paper, Wavelet Transform, Fractional Fourier Transform (FrFT) and Fractional Cosine Transform (FrCT) are compared using Mean Square Error (MSE) and Peak signal-toNoise Ratio (PSNR) in the field of image compression. Wavelet provides better MSE and PSNR at lower Compression Ratio (CR), whereas FrFT provides good result at higher CR and FrCT provides same results as that of Wavelet at hig...

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...

As many traditional de-noising methods fail in the intensive noises environment and are unadaptable in various noisy environments, a method of speech enhancement has been advanced based on dynamic Fractional Fourier Transform (FRFT)filtering. The acoustic signals are framed. The renewing methods are put in FRFT optimal disperse degree of noising speech and this method is implemented in detail. ...

We present a new method of beamforming using the fractional Fourier transform (FrFT). This method encompasses the conventional minimum mean-squared error (MSE) beamforming in the frequency domain or spatial domain as special cases. It is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating sinusoidal sources where the Doppler effect ge...

In this paper we present a time-frequency approach for acoustic seabed classification. Work reported is based on sonar data collected by the Volume Search Sonar (VSS), one of the five sonar systems in the AN/AQS-20. The Volume Search Sonar is a beamformed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back ...

Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of the phase-space: no linear structure is necessary. It is shown that the “fractional Fourier transform” provides a simple example of this construction. As an ap...

In this paper, we propose an optical image watermarking scheme using the fractional Fourier transform. A two-dimensional watermark is encrypted using a double random fractional order Fourier domain encoding technique. The encrypted image is watermarked into a three-dimensional intensity image reconstructed from a real in-line digital hologram. The watermark is recovered by applying the correspo...

Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time t, the Hankel transform with respect to the radial coordinate r, the finite Fourier transform with respect to the angular coordinate φ, and the exponential Fourier transfor...