Finite impulse response

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A finite impulse response (FIR) filter is a type of a digital filter. It is 'finite' because it's response to an impulse ultimately settles to zero. This is in contrast to infinite impulse response filters which have internal feedback & may continue responding indefinitely. The transfer function of an FIR filter has zeros and has N poles at the origin: The transfer function is $H(z)=b_{0}+b_{1}z^{-1}+...+b_{N}z^{-N}$$={\frac {B(z)}{z^{N}}}$. FIR filters are also known as moving average filters (MA). The difference equation is $y\left[k\right]=b_{0}u\left[k\right]+b_{1}u\left[k-1\right]=...+b_{N}u\left[k-N\right]$ The impulse response is $h\left[0\right]=b_{0},h\left[1\right]=b_{1},...,h\left[N\right]=b_{N},h\left[N+1\right]=0,...$

Properties

A FIR filter has a number of useful properties which sometimes make it preferable to an infinite impulse response filter:

• FIR filters are inherently stable
• Require no feedback
• Can have linear phase
• Can have minimum phase

Filter design

You can design FIR filters by optimization (Weighted Least Squares Design, Minimax Design) or in practice ('Windows',Equiripple design, Software like Matlab)

See also

• Digital filter
• Electronic filter
• Filter (signal processing)
• Infinite impulse response
• Z-transform (specifically Z-transform#LCCD equation)
• Filter design

==External links==

http://www.dspguru.com/info/faqs/fir/basics.htm