Related papers: An Integer Approximation Method for Discrete Sinus…

Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…

A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…

A new multiplication-free transform derived from DHT is introduced: the RHT. Investigations on the properties of the RHT led us to the concept of weak-inversion. Using new constructs, we show that RHT is not involutional like the DHT, but…

This report elaborates on approximations for the discrete Fourier transform by means of replacing the exact Cooley-Tukey algorithm twiddle-factors by low-complexity integers, such as $0, \pm \frac{1}{2}, \pm 1$.

This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point…

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier…

This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the…

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…

The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…

Real-valued block codes are introduced, which are derived from Discrete Fourier Transforms (DFT) and Discrete Hartley Transforms (DHT). These algebraic structures are built from the eigensequences of the transforms. Generator and parity…

In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using…

Self-attention is central to the success of Transformer architectures; however, learning the query, key, and value projections from random initialization remains challenging and computationally expensive. In this paper, we propose two…

With the integration of communication and computing, it is expected that part of the computing is transferred to the transmitter side. In this paper we address the general problem of Frequency Modulation (FM) for function approximation…

This work presents a highly optimized computational framework for the Discrete Dipole Approximation, a numerical method for calculating the optical properties associated with a target of arbitrary geometry that is widely used in…

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

The two-dimensional discrete cosine transform (DCT) can be found in the heart of many image compression algorithms. Specifically, the JPEG format uses a lossy form of compression based on that transform. Since the standardization of the…

Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational…

Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…

The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…

We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…