Finite Impulse Response Filters

Finite impulse response (FIR) filters are digital filters, which have a finite impulse response. FIR filters are also known as nonrecursive filters, convolution filters, or moving-average (MA) filters because you can express the output of an FIR filter as a finite convolution

,

where x represents the input sequence to be filtered, y represents the output filtered sequence, and h represents the FIR filter coefficients.

The following list gives the most important characteristics of FIR filters:

,

where n is the number of FIR filter coefficients.

The following graphs plot a typical magnitude and phase response of FIR filters versus normalized frequency.

The discontinuities in the phase response arise from the discontinuities introduced when you compute the magnitude response using the absolute value. Notice that the discontinuities in phase are on the order of pi. The phase, however, is clearly linear. Refer to Signal Processing Related Documentation for material that can give you more information on this topic.

You design FIR filters by approximating a specified, appropriate frequency response of a discrete-time system. The most common techniques approximate the appropriate magnitude response while maintaining a linear-phase response.