Signal Processing Toolbox

FIR Filter Design

Digital filters with finite-duration impulse response (all-zero, or FIR filters) have both advantages and disadvantages compared to infinite-duration impulse response (IIR) filters.

FIR filters have the following primary advantages:

• They can have exactly linear phase.
• They are always stable.
• The design methods are generally linear.
• They can be realized efficiently in hardware.
• The filter startup transients have finite duration.

The primary disadvantage of FIR filters is that they often require a much higher filter order than IIR filters to achieve a given level of performance. Correspondingly, the delay of these filters is often much greater than for an equal performance IIR filter.

Filter Method	Description	Filter Functions
Windowing	Apply window to truncated inverse Fourier transform of desired "brick wall" filter	fir1, fir2, kaiserord
Multiband with Transition Bands	Equiripple or least squares approach over sub-bands of the frequency range	firls, firpm, firpmord
Constrained Least Squares	Minimize squared integral error over entire frequency range subject to maximum error constraints	fircls, fircls1
Arbitrary Response	Arbitrary responses, including nonlinear phase and complex filters	cfirpm
Raised Cosine	Lowpass response with smooth, sinusoidal transition	firrcos

Comparison of Classical IIR Filter Types

Linear Phase Filters

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