An overview of the methods of synthesis, realization and implementation of orthogonal 3-D rotation filters and possibilities of further research and development

In the paper, an overview of the methods and algorithms of synthesis, realization and implementation used by the author to obtain orthogonal 3-D filters with a structure made of Givens rotations has been presented. The main advantage of orthogonal filters, which may have a lower sensitivity to quantization of the coefficients, was indicated. The author proposed a number of possible changes and modifications of individual stages, which may result in obtaining filters with even better parameters. The work will be the basis for the direction of further research

Convolutional Neural Networks as 2-D systems

This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of linear filters, is realized in state space as a linear time-invariant 2-D system. The overall convolutional Neural Network composed of convolutional layers and nonlinear activation functions is then viewed as a 2-D version of a Lur'e system, i.e., a linear dynamical system interconnected with static nonlinear components. One benefit of this 2-D Lur'e system perspective on CNNs is that we can use robust control theory much more efficiently for Lipschitz constant estimation than previously possible

Relationships between digital signal processing and control and estimation theory

Bibliography: leaves 83-97.NASA Grant NGL-22-009-124 and NSF Grant GK-41647.Alan S. Willsky

A Stand-alone Station and DSP Method for Deep Sky Objects Astrophotography

This article presents the basic assumptions and aspects of the design of a stand-alone station for deep sky objects (DSO) astrophotography. It describes the main elements of a project concerned with automatization, remote control and auto-guiding [1-5] of a system. The article also covers in further detail the innovative use of a driver with an ATMEGA16 microcontroller and dedicated software for controlling the astronomical dome and its synchronization with telescope movement. Furthermore, a new concept of reprogrammable digital circuit implementation for auto-guiding systems is shown, which operates with a popular CCD webcam and ST4 compatible equatorial mounts. This idea was verified by the circuit prototype implemented on an Altera Cyclone II FPGA device and tested with real sky objects. A fully functional solution for performing automatic observation is presented. The project was also designed for amateur-astronomy, and therefore, user-friendly configuration and maintenance constituted very important factors, which were taken into consideration

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Linear image filtration based on loss-less structures

W artykule przedstawiono nową technikę implementacji filtrów dwuwymiarowych. Polega ona na rozkładzie macierzy modelu Roessera na kaskadowe połączenie rotatorów Givens'a. Dzięki nowatorskiemu zastosowaniu permutacji otrzymuje się strukturę potokową o dużej odporności na błędy obliczeń o skończonej precyzji.In this paper, a novel two-dimensional FIR filter implementation technique is presented. It is based on a concept of orthogonal filters known from 1-D domain. The key of the algorithm is to represent a 2-D system as a cascade connection of two 1-D systems, which are described by 1-D transfer function vectors, given by (7). Each 1-D system is transformed into an orthogonal system via the synthesis of a paraunitary transfer matrix [5]. As a result, one obtains a cascade connection of two 1-D systems described by orthogonal state-space equations. Then, the equations can be combined to form orthogonal Roesser model matrices (14), and can be implemented using Givens Rotations and delay elements. The technique is illustrated by an example of an edge detection kernel filter whose convolution matrix is given by (15). Following the algorithm presented in the paper, there was obtained the Roesser model (22) and its decomposition into the cascade connection of Givens rotations whose parameters are collected in Tab 1. It was implemented using Audio Video Development Kit Stratix II GX. Givens rotation blocks were built by means of DSP blocks available in FPGA chip. Additionally, a system that realizes the same convolution matrix (15), but based on a direct structure (nine multipliers), was built for comparable purposes. Two tests were performed: an impulse response and sensitivity of frequency response to coefficient changes. The impulse response of both systems is the same up to finite precision errors. The sensitivity is much lower for the rotation structure (Fig. 2) when compared to the direct structure (Fig. 3)