Related papers: The Basic Discrete Hilbert Transform with an Infor…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
In this paper, a new waveform called discrete Fourier transform spread orthogonal frequency division multiplexing with chirp modulation (DFT-s-OFDM-CM) is proposed for the next generation of wireless communications. The information bits are…
Reversible data hiding (RDH) is one special type of information hiding, by which the host sequence as well as the embedded data can be both restored from the marked sequence without loss. Beside media annotation and integrity…
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In…
This paper presents a new discrete Hilbert transform (DHT) based measure of randomness for discrete sequences. The measure has been used to test three different classes of sequences with satisfactory results.
Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{2 \pi i\alpha m^2} f(n - m)}{m}. $$ We prove that, uniformly in $\alpha \in…
Data hiding is the art of hiding secret data into a cover object such as digital image for covert communication. In this paper, we make the first step towards hiding ``data hiding'', which is totally different from many conventional works…
A many to one discrete auditory transform is presented to map a sound signal to a perceptually meaningful spectrum on the scale of human auditory filter band widths (critical bands). A generalized inverse is constructed in closed analytical…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
We consider a private discrete distribution estimation problem with one-bit communication constraint. The privacy constraints are imposed with respect to the local differential privacy and the maximal leakage. The estimation error is…
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for…
We demonstrate combined high-fidelity long-haul transfer of a linearly chirped, optical frequency and time transfer. In a proof-of-principle experiment we transfer an optical frequency with a linear chirp of around 238 kHz/s via a…
A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the…
In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
Data hiding is the art of concealing messages with limited perceptual changes. Recently, deep learning has enriched it from various perspectives with significant progress. In this work, we conduct a brief yet comprehensive review of…
Dissipative cat qubits are known for the exponential suppression of the bit-flip rate. However, there is significant discrepancy between experimental measurements and analytical predictions of the strength of the bit-flip suppression. In…
Differential privacy is becoming one gold standard for protecting the privacy of publicly shared data. It has been widely used in social science, data science, public health, information technology, and the U.S. decennial census.…