Orthogonal transforms and their application to image coding

Imperial Users onl

Radix-2² Algorithm for the Odd New Mersenne Number Transform (ONMNT)

\ua9 2023 by the authors. This paper introduces a new derivation of the radix- (Formula presented.) fast algorithm for the forward odd new Mersenne number transform (ONMNT) and the inverse odd new Mersenne number transform (IONMNT). This involves introducing new equations and functions in finite fields, bringing particular challenges unlike those in other fields. The radix- (Formula presented.) algorithm combines the benefits of the reduced number of operations of the radix-4 algorithm and the simple butterfly structure of the radix-2 algorithm, making it suitable for various applications such as lightweight ciphers, authenticated encryption, hash functions, signal processing, and convolution calculations. The multidimensional linear index mapping technique is the conventional method used to derive the radix- (Formula presented.) algorithm. However, this method does not provide clear insights into the underlying structure and flexibility of the radix- (Formula presented.) approach. This paper addresses this limitation and proposes a derivation based on bit-unscrambling techniques, which reverse the ordering of the output sequence, resulting in efficient calculations with fewer operations. Butterfly and signal flow diagrams are also presented to illustrate the structure of the fast algorithm for both ONMNT and IONMNT. The proposed method should pave the way for efficient and flexible implementation of ONMNT and IONMNT in applications such as lightweight ciphers and signal processing. The algorithm has been implemented in C and is validated with an example

Digital Signal Processing

Contains reports on twelve research projects.U. S. Navy - Office of Naval Research (Contract N00014-75-C-0951)National Science Foundation (Grant ENG76-24117)National Aeronautics and Space Administration (Grant NSG-5157)Joint Services Electronics Program (Contract DAABO7-76-C-1400)U.S. Navy-Office of Naval Research (Contract N00014-77-C-0196)Woods Hole Oceanographic InstitutionU. S. Navy - Office of Naval Research (Contract N00014-75-C-0852)Department of Ocean Engineering, M.I.T.National Science Foundation subcontract to Grant GX 41962 to Woods Hole Oceanographic Institutio

The deep space network

Network engineering, hardware and software development, and tracking station operations for support of deep space unmanned flight projects are summarized

Ultrasound Imaging

In this book, we present a dozen state of the art developments for ultrasound imaging, for example, hardware implementation, transducer, beamforming, signal processing, measurement of elasticity and diagnosis. The editors would like to thank all the chapter authors, who focused on the publication of this book

Efficient Multiplication of Somewhat Small Integers using Number-Theoretic Transforms

Conventional wisdom purports that FFT-based integer multiplication methods (such as the Schönhage-Strassen algorithm) begin to compete with Karatsuba and Toom-Cook only for integers of several tens of thousands of bits. In this work, we challenge this belief, leveraging recent advances in the implementation of number-theoretic transforms (NTT) stimulated by their use in post-quantum cryptography. We report on implementations of NTT-based integer arithmetic on two Arm Cortex-M CPUs on opposite ends of the performance spectrum: Cortex-M3 and Cortex-M55. Our results indicate that NTT-based multiplication is capable of outperforming the big-number arithmetic implementations of popular embedded cryptography libraries for integers as small as 2048 bits. To provide a realistic case study, we benchmark implementations of the RSA encryption and decryption operations. Our cycle counts on Cortex-M55 are about 10× lower than on Cortex-M3

Numerical and experimental comparison among a new hybrid FT-music technique and existing algorithms for through-the-wall radar imaging

A fast low-cost through-the-wall radar imaging (TWRI) system, based on a vector network analyzer (VNA), a couple of switches and an array of Vivaldi antennas, has been designed, realized, and tested. To solve the TWRI inversion problem, an original theoretical modeling for a class of TWRI techniques whose basic functions are the cross-range Fourier transform (FT) of the scattered field and its covariance operator has been proposed. Using these functions, four conventional algorithms, namely the delay and sum (DAS), the FT, the multiple signal classification (MUSIC), the hybrid DAS-MUSIC and a new algorithm, the hybrid FT-MUSIC, have been derived. All these techniques have been implemented and their accuracy and field of view have been tested on canonical scatterers. Then, the algorithms have been applied to measured data collected in different scenarios constituted by a metallic bar or a human subject in the absence and in the presence of a wall between the antenna and the considered targets. Using the proposed TWRI system, it has been possible to detect a subject located up to 5-m away from the radar antenna array through a tuff wall. The proposed FT-MUSIC algorithm has evidenced performances similar to those of the DAS-MUSIC but with significantly lower execution times. Finally, FT-MUSIC performances in terms of field of view and immunity to disturbances are better compared to those of the MUSIC algorithm