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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