FIR filters are defined by an impulse response that has finite duration; that is, it settles to zero in a finite amount of time. This behavior contrasts with IIR filters, which may continue responding indefinitely due to internal feedback. The absence of feedback in FIR filters makes them a preferred choice for applications where phase linearity and stability are critical requirements.
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Finite Impulse Response (FIR) filters are a fundamental component of modern digital signal processing. While they may require higher computational power than their IIR counterparts to achieve sharp cutoffs, their guaranteed stability and ability to provide a linear phase response make them indispensable in sensitive applications. As computational resources continue to become cheaper and more powerful, the use of FIR filters in embedded systems and real-time processing is likely to expand further, cementing their role as a versatile and reliable tool for signal manipulation. FIR filters are defined by an impulse response
$$ H(z) = \sum_k=0^N h[k] z^-k $$
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