FPGA Implementation of Very Sharp FIR Filters Obtained by Frequency-Response Masking Technique

Proučena je tehnika maskiranja frekvencijske karakteristike (FRM) za dobivanje vrlo strmih niskopropusnih FIR filtara s linearnom fazom. FRM tehnikom su obuhvaćeni i uskopojasni i širokopojasni filtri. Za realizaciju FRM filtra određeni su prototipni i maskirni filtri te faktor skaliranja frekvencijske osi. Za dane granične frekvencije prijelaznog područja FRM filtra razvijen je postupak određivanja faktora skaliranja te graničnih frekvencija prototipnog filtra i graničnih frekvencija maskirnih filtara. Za dobivene frekvencije te za dane redove ovih filtara određeni su koeficijenti njihovih prijenosnih funkcija koje imaju jednoliku valovitost amplitude u području propuštanja i području gušenja. Za potrebe implementacije FRM filtra razvijen je fizički ostvariv model FIR filtra korištenjem jednog zbrajala i jednog mmnožila, koji podržava generički broj elemenata za kašnjenje između dvije uzastopne sumacije. Korištenjem ovog modela i dobivenih koeficijenata implementiran je prototipni filtar s brojem elemenata za kašnjenje koji odgovara faktoru skaliranja te maskirni filtri s jediničnim kašnjenjem. Na kraju, korištenjem ovih filtara, razvijen je model širokopojasnog FRM filtra. Model filtra razvijen je u jeziku VHDL i uhodan na razvojnom sustavu Zedboard.The frequency response masking (FRM) technique has been studied to obtain very steep non-linear FIR filters with a linear phase. FRM technology included narrowband and wideband filters. For the FRM filter, prototype and masking filters and the frequency axis scaling factor were determined. For given FRM filter cutoff frequencies, the method of determining the scaling factor and the prototype filter and masking filters boundary frequencies has been developed. For the obtained frequencies and for given orders of these filter, the coefficients of the transfer functions were determined, which have a uniform amplitude wavelength in the passband and stopband area. For the implementation of the FRM filter, a physically feasible FIR filter model was developed using one adder and one multiplier, which supports a generic number of delay elements between two successive additions. By using this model and the obtained coefficients, a prototype filter with a number of delay elements corresponding to the scaling factor and the single-delay masking filters were implemented. Finally, using these filters, a wideband FRM filter model was developed. The filter model was developed in VHDL language and run on the Zedbord development system