Practical Design of Digital Filters Using the Pascal Matrix

Abstract

IN THE CONTEXT OF THE DE SIGN OF DIGITAL FILTERS MANY RESEARCH HAS BEEN DONE TO FACILITATE THEIR COMPUTATION. THE PASCAL MATRIX RECENTLY DE FINED IN (BIOLKOVA AND BIOLEK, 1999) HAS PROVED ITS UTILITY IN THIS FIELD. IN THIS PAPER WE SUMMARIZE THE DIRECT TRANSFORM FROM THE LOWPASS CONTINUOUS-TIME TRANSFER FUNCTION H(S) TO THE DISCRETE-TIME H(Z) OF THE FOLLOW INGMAIN TREE TYPES OF DIGITAL FILTERS: LOWPASS, HIGHPASS AND BANDPASS. AN ALTERNATIVE REPRESENTATION OF THE ORIGINAL BANDPASS PASCAL MATRIX IS DEVELOPED IN THIS PAPER THAT PERMITS TO CONVERT SYSTEM AT ICALLY THE LOWPASS CONTINUOUS-TIME PROTOTYPE TO THE DISCRETE-TIME BANDPASS TRANSFER FUNCTION. WE ALSO CONSIDER THE IN VERSE TRANSFORMATION FROM THE DISCRETE-TIME DOMAIN TO THE CONTINUOUS ONE AND WE SHOW THAT THE IN VERSE TRANSFORMATION IS EASILY OB TAINED AS THE DETERMINANT OF THE SYSTEM NEED NOT TO BE COMPUTED. SEVERAL NUMERICAL EXAMPLES ILLUSTRATE THE PRACTICAL UTILIZATION OF THIS TECHNIQUE.