Preface

The original Italian document, "Un sistema numerico per misure in tempo reale", was a doctoral thesis in Electronics Engineering, written in the spring of 1993 by Davide Allegri and Giorgio Cavalli, at the "Politecnico di Milano" (Italy). Although the system used at that time is now obsolete, the math behind it and the algorithms are still in use and of interest. The present edition has been translated in English by Davide Allegri, who would welcome any comment, suggestion by the reader

Index

1: INTRODUCTION

2: SYSTEM OVERVIEW

 2.1 INTRODUCTION

 2.2 HARDWARE DESCRIPTION

 2.3 SIGNAL PROCESSOR ARCHITECTURE

 2.4 DSP MEMORY MAP

 2.5 SOFTWARE ENVIRONMENT

 2.6 COMMUNICATION BETWEEN UNITS

3: INFINITE IMPULSE RESPONSE FILTER IIR

 3.1 FILTER INTRODUCTION

 3.2 INFINITE IMPULSE RESPONSE FILTER IIR

 3.3 IIR FILTER PROPERTIES

 3.3.1 BUTTERWORTH

 3.3.2 CHEBYSHEV FILTER

 3.3.3 ELLIPTIC FILTERS

 3.4 STRUCTURE

 3.5 A UNIVERSAL FILTERING SYSTEM IMPLEMENTATION

 3.6 EXPERIMENTAL RESULTS

4: FINITE IMPULSE RESPONSE FILTER FIR

 4.1 INTRODUCTION

 4.2 FIR FILTER IMPLEMENTATION

 4.3 STRUCTURE

 4.4 INSTRUMENT IMPLEMENTATION

 4.5 EXPERIMENTAL RESULTS

5: THE FAST FOURIER TRANSFORM

 5.1 INTRODUCTION

 5.2 THE OPTIMAL SOLUTION

 5.3 TIME DECIMATION RADIX-2 FFT

6: A NEW APPROACH TO THE FFT

 6.1 INTRODUCTION

 6.2 FFT OF A PERIODIC SIGNAL

 6.3 THE IMPLEMENTED ALGORITHM

 6.4 THE IMPLEMENTED WINDOWS

 6.5 LABVIEW ALGORITHMS

 6.6 DSP ALGORITHMS

 6.7 EXPERIMENTAL RESULTS

7: CONCLUSIONS

Introduction

The goal of the actual work is to develop digital signal processing algorithms for real time applications. In particular, the Finite Impulse Response (FIR), the Infinite Impulse Response (IIR) filters, and a software instrument that is able to perform spectral analyses in real time, on eight input channels at the same time.

In this document, with the term real time measurement we mean a measure performed in a range of time small enough to allow a proper view of the whole phenomenon of interest, and its dynamic evolution without any loss of information.

About the measurement algorithms, we focus our attention on methods that minimise the errors for the Fast Fourier Transforms (FFTs). In particular, we implemented an algorithm [1], which minimises the phase spectral error.

The main feature of this algorithm, here implemented for the first time in a real time instrument, is the way in which it minimises the phase error: the procedure is based on data symmetry characteristics rather than the well known interpolation methods. These latter methods are often more complex and a good degree of efficiency is achieved only under particular conditions (like a negligible harmonic interference) [2].

All the designed algorithms have been implemented and tested on an acquisition computer based system. The programming language used has been a graphical one based on traditional languages. The main advantage of this language is the ability to write code just drawing Block Diagrams, each of them, representing the different algorithm, and Link Lines, representing the paths followed by the digital signals, during the processing time.

Another feature of the system is that is able to represent and display the front panel of a traditional measurement instrument, from both a graphical and instrument control point of view. It is for these reasons we defined it as a VIRTUAL INSTRUMENT.