SYNTHESIS AND POLYPHASE
IMPLEMENTATION OF wide-band LOW-PASS CIRCULAR 2D FIR FILTERS
Doru Florin CHIPER[1], Radu MATEI[2]
Rezumat. Se propune o tehnică de proiectare analitică n domeniul frecvenţă
pentru filtre 2D de tip FIR
trece jos de bandă largă cu simetrie circulară. Proiectarea este bazată pe un fitru prototip trece-jos, ideal de
maxim plat, cu banda de trecere
specificată, derivat
din funcţia tangentă
hiperbolică. Prototipul
ideal este aproximat cu un polinom trigonometric, printr-o schimbare de variabilă şi dezvoltare n serie Chebyshev, astfel rezult nd răspunsul n frecvenţă factorizat al
prototipului 1D. Aplicand prototipului o transformare de frecvenţă specifică,
derivată din transformarea
generală McClellan, va
rezulta direct răspunsul
n frecvenţă al filtrului 2D circular dorit, de asemenea factorizat. Filtrul proiectat are o formă precisă, cu distorsiuni neglijabile. S-a propus de asemenea şi o implementare eficientă la nivel de sistem pentru filtrul
proiectat, utiliz nd metoda de descompunere polifazică şi filtrare pe blocuri, ce duce la o structură
de filtrare eficientă,
cu complexitate aritmetică
redusă şi un grad
ridicat de paralelism.
Abstract. An analytical synthesis technique in the frequency domain is proposed for a
particular class of 2D filters, namely circular wide-band low-pass FIR filters.
The design starts from a low-pass prototype filter which is ideally maximally
flat, with specified bandwidth, based on hyperbolic tangent function. This is
approximated as a trigonometric polynomial using a change of variable and the
Chebyshev series, thus obtaining the factored frequency response of the FIR
filter prototype. Applying a specific frequency mapping derived from the more
general McClellan transform, the frequency response of the desired circular 2D
FIR filter results directly, also in factored form. The designed filter has an
accurate shape, with negligible distortions. We also proposed a computationally efficient implementation at
system level, based on polyphase decomposition and block filtering approach,
which leads to a filtering structure with low aritmetic
complexity and a high degree of parallelism.
Keywords: 2D FIR filters, circular filters,
approximations, analytic design, polyphase filtering
DOI 10.56082/annalsarsciinfo.2024.1.60
[1] Prof., Faculty of Electronics, Telecommunications and Information
Technology, Technical University Gheorghe Asachi , Iasi,
Romania; Academy
of Romanian Scientists - AOSR; Technical Sciences Academy of Romania ASTR (e-mail: chiper@etti.tuiasi.ro).
[2]Lecturer, PhD, Faculty of Electronics, Telecommunications and Information Technology, Technical University Gheorghe Asachi , Iasi, Romania, Institute of Computer Science, Romanian Academy Iaşi Branch (rmatei@etti.tuiasi.ro).