Robustness is a key attribute of spread spectrum (SS) watermarking scheme. It is significantly deteriorated if one tries to achieve high embedding rate keeping other parameters unaltered. In literatures, typically various transformations like DFT, DCT, Fourier–Mellin and wavelet are used for SS multimedia watermarking but little studies have been attempted so far to see what are the possible fa...

1. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on R n (n = 3) 3. Fourier inversion on R 2 4. Fourier inversion on R n (general n) 5. Fourier inversion on spheres 6. Fourier inversion on complex projective space, and variants 7. Fourier inversion on hyperbolic space, and variants 8. Fourier inversion on strongly scattering manifolds 9. Hermite expansions an...

In this paper, we examine the theory of motion-free superresolution by formulating the problem in the Discrete Time Fourier Transform (DTFT) and the Discrete Fourier Transform (DFT) domain. Our approach provides some new insights into how aliasing and blurring can effect exact reconstruction of the superresolved image. For ease of understanding, the analysis, is initially carried out in the 1-D...

Fractional Fourier transform (FRFT) performs a rotation of signals in the time—frequency plane, and it has many theories and applications in time-varying signal analysis. Because of the importance of fractional Fourier transform, the implementation of discrete fractional Fourier transform will be an important issue. Recently, a discrete fractional Fourier transform (DFRFT) with discrete Hermite...

-Fractional Fourier Transform is a generalization of the classical Fourier Transform, which has found its most useful applications for the transient analysis of the signals. This paper studies the span of the Fractional Fourier Transform in relation with the amplitude and phase functions of the signal and provides a mathematical derivation for the generalized case. The derived expression is sho...

7 Trigonometric Identities, Complex Exponentials and Periodic Sequences 26 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 26 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 28 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 29 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 31 7.5 The Exponential of a Complex Numbe...