Systolic processing of digital signals

The huge demand for fast techniques for processing large amounts of data has contributed to the emergence of hitherto unknown concepts of time-space algorithms, as well as new hardware solutions resulting from the rapidly growing global technologies.

One of the solutions are special types of so-called systolic boards. SYSTOLIC PANELS are multiprocessor systems of special applications in which time-space algorithms are closely matched to the hardware architecture. The computational efficiency of systolic tables is the result of parallel and pipelined processing.

The monograph is divided into three parts. The first discusses basic systolic algorithms in application to the problems of matrix algebra, multiplication and division of polynomials, weave operations, discrete transforms and artificial neural networks. The second part discusses the use of signal flow graphs and graphs for the design of systolic boards. It is based on the developed original method of designing VLSI circuits. The third part presents the basic features that should be characterized by systolic tables for the problems of mathematical morphology.

The monograph is intended for students, PhD students and specialists in the field of various scientific disciplines, such as IT specialists and electronic engineers who deal with signal processing and their application.

Table of Contents

Part I. Theory

1. Introduction

1.1. Definition
1.2. Examples of classic architectures
1.3. Examples of applications and implementation

2. Multiplying the matrix by vector

3. Multiplying matrix by matrix

3.1. Hexagonal tables
3.2. Orthogonal tables

4. Transformation of the complete matrix into a band matrix

5. Systolic realizations of the weave

5.1. Classic systolic realizations of the weave
5.2. The design procedure for 2D and 3D weave, using classical systolic tables for 1D weave
5.3. Schematic representation of the design procedure for the implementation of the systolic 2D and 3D weave operations

6. Solving systems of linear equations

6.1. Triangular distribution of the matrix
6.2. Solving a system of linear equations using a linear systolic array

7. Discrete transforms

7.1. A systolic implementation of one-dimensional discrete Fourier transform
7.2. Two-dimensional discrete Fourier transofrata and its systolic representation
7.3. Schematic representation of the design procedure for the implementation of the systolic 1D and 2D DFT
7.4. Discreet Walsh-Hadamard Transform

8. Systolic implementation of multiplication and division of polynomials

8.1. Introduction
8.2. Systolic executions using linings
8.3. Other systolic realizations
8.4. Systolic realizations of dividing polynomials

9. Systolic implementation of the neural network

9.1. Multilayer neural network
9.2. Systolic simulation of the neural network
9.3. Learning using the back error propagation algorithm
9.4. Implementation of the learning procedure on the systolic table

10. Summary

Literature

Part II. Designing systolic tables using graphs

11. Introduction

12. Theory of designing systolic tables

12.1. Dependency graphs
12.2. Signal flow graph
12.3. SFG systolization
12.4. Construction of a systolic board
12.5. Modifications
12.6. Basic parameters of systolic boards
12.7. optimization

13. Table design - examples

13.1. Weave
13.2. Discrete transforms
13.3. Solving systems of linear equations

Literature

Part III. Systolic implementation of mathematical morphology operations

14. Introduction

15. Mathematical morphology

16. The concept of a systolic array for morphological processing

16.1. Mathematical morphology of the image using the systolic array concept
16.2. Design of a systolic array for morphological operations

17. Inserting the image into the systolic board

17.1. The location of the entered image in the systolic table
17.2. Data input from one direction
17.3. The issue of image size in relation to the size of the systolic array
17.4 Further suggestions for the board to be modified

18. Systolic algorithms for morphological operations on the image

19. The systolic implementation of mofrological operations

19.1. Method 1
19.2. Method 2
19.3. Method 3
19.4. Transformation Hit-and-Miss
19.5. Opening and closing operations
19.6. Transfrmations White Top Hat and Black Top Hat
19.7. Extraction of the border

20. Examples of the use of mathematical morphology algorithms

21. Scalability and acceleration coefficient of systolic time-space algorithms

22. Summary

Literature