A finite impulse response (FIR) system is a type of a [[discrete-time LTI system]] where the output depends only on a finite number of input samples. It is also known as an FIR filter. The [[difference equation]] of an FIR system depends only on the current and past values of the input signal $x(n)$: $ y(n) = \sum_{k=0}^{M} b_k x(n-k) $ In an FIR system the $b_{k}$ coeficients are the samples of [[impulse response]] of the system: $ h(n) = b_{n} $ The FIR system can be represented with the following graph: ![[fir-fdir.svg|600]] FIR filters can have a linear phase response, which means that they do not introduce any phase shift in the filtered signal. They are widely used in various applications such as audio and image processing, communication systems, and biomedical signal analysis. In the general case, [[discrete-time LTI system]]s have an [[infinite impulse response (IIR) system]].