Related papers: Approximate Computation of DFT without Performing …
A technique is presented for producing synthetic images from numerical simulations whereby the image resolution is adapted around prominent features. In so doing, adaptive image ray-tracing (AIR) improves the efficiency of a calculation by…
Linear detectors such as zero forcing (ZF) or minimum mean square error (MMSE) are imperative for large/massive MIMO systems for both the downlink and uplink scenarios. However these linear detectors require matrix inversion which is…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm…
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…
Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we…
Radar sensors play a crucial role for perception systems in automated driving but suffer from a high level of noise. In the past, this could be solved by strict filters, which remove most false positives at the expense of undetected…
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…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
Recent years have seen renewed attention to arithmetic coding (AC). This is thanks to the use of AC for distribution matching (DM) to control the channel input distribution in probabilistic amplitude shaping. There are two main problems…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…
A transmitted, unknown radar signal is observed at the receiver through more than one path in additive noise. The aim is to recover the waveform of the intercepted signal and to simultaneously estimate the direction of arrival (DOA). We…