Filtro digital

Um filtro tem como função remover partes não desejadas de um sistema de transmissão ou extrair partes que podem ser útil do sinal. O filtro digital é um filtro que processa sinais digitais usando um processador digital para executar cálculos necessários para fazer a filtragem, multiplicando os valores da entrada por constantes e somando os produtos resultantes, além de utilizar técnicas matemáticas, como Transformadas de Fourier e Hilbert em valores amostrados do sinal de entrada. O processador pode ser um computador ou um DSP. Em um processo de filtragem digital, o sinal analógico deve ser primeiramente digitalizado usando um ADC.^[1] Filtros digitais são um elemento essencial para os atuais equipamentos eletrônicos, como rádios, celulares e dispositivos multimídia em geral.

Tipos

Filtro FIR - Filtro FIR (FIR – Finite Impulse Response) é um filtro digital que apresenta duração finita em resposta a um impulso;^[2]
Filtro IIR - Filtro IIR (IIR – Infinite Impulse Response) é um filtro digital que apresenta duração infinita em resposta a um impulso.^[3]


REPRESENTAÇÃO DE UM FILTRO IIR	$y[n]=a_{n}x[n]+a_{n-1}x[n-1]+a_{n-2}x[n-2]+...+b_{n-1}y[n-1]+b_{n-2}y[n-2]+...$
REPRESENTAÇÃO DE UM FILTRO FIR	$y[n]=a_{n}x[n]+a_{n-1}x[n-1]+a_{n-2}x[n-2]+a_{n-3}x[n-3]+...$

x[ ] é o sinal de entrada;
y[ ] é o sinal de saída;
a e b são os coeficientes de recursão. ^[4]

Para achar o coeficientes de recursão e a resposta do filtro de um filtro IIR é necessário utilizar a técnica matemática chamada de Transformada Z.

Vantagens

Os filtros digitais têm muitas vantagens comparativamente aos analógicos. Por exemplo:

A durabilidade dos componentes electrónicos que constituem um filtro analógico é muito menor que a durabilidade do equipamento de aquisição e processamento de sinal que constitui o filtro digital;
Consegue-se facilmente implementar filtros de ordem elevada;
O SNR (a relação sinal-ruído, signal-to-noise ratio em inglês, que é a relação entre a potência do sinal e a potência do ruído) dos filtros digitais é muito maior;
Os filtros digitais são facilmente projetados, sendo os mesmos testados e implementados em um computador de forma simples;
Como filtros digitais são programável a sua operação é determinada por um programa armazenado na memória de um processador. Isto significa que o filtro digital pode ser mudado facilmente sem afetar seu circuito eletrônico (hardware).^[5]

Ver também

Referências

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