# firlpnorm (Digital Filter Design Toolkit, MathScript Function)

**Owning Class: **singlerate

## Syntax

b = firlpnorm(n, f, e, mag)

b = firlpnorm(n, f, e, mag, w)

b = firlpnorm(n, f, e, mag, w, p)

[b, err] = firlpnorm(n, f, e, mag)

[b, err] = firlpnorm(n, f, e, mag, w)

[b, err] = firlpnorm(n, f, e, mag, w, p)

## Description

Designs a finite impulse response (FIR) filter that uses the least p-th norm algorithm to approximate the frequency response you specify.

## Inputs

Name |
Description |

n |
Specifies the order of the filter. n is a nonnegative integer. |

f |
Specifies the frequency points. f is a vector whose values increase monotonically between 0 and 1. |

e |
Specifies the band edge frequencies. e is a vector whose values must also exist in f. |

mag |
Specifies the magnitude response of the filter at f. mag is a vector of the same length as f. |

w |
Specifies the weight of each frequency point. w is a vector of the same length as f. The default is a vector in which each element has a value of 1. |

p |
Specifies the value of p to use in the least p-th norm algorithm. p is a positive integer that must fall in the range [1, 128]. The default is 128. |

## Outputs

Name |
Description |

b |
Returns the coefficients of the designed FIR filter. b is a real vector with a length of n+1. |

err |
Returns the least p-th norm approximation error. err is a real number. |

## Examples

b = firlpnorm(40, [0, 0.2, 0.5, 0.6, 1], [0, 0.5, 0.6, 1], [1, 2, 1, 0, 0]);fft_mag = abs(fft(b, 16384));

figure;

plot(0:1/8192:1, fft_mag(1:8193));

b = firlpnorm(22, [0, 0.4, 0.6, 1], [0, 0.4, 0.6, 1], [1, 1, 0, 0], [1, 1, 1, 1], 2);

figure;

freqz(b);

b = firlpnorm(22, [0, 0.4, 0.6, 1], [0, 0.4, 0.6, 1], [1, 1, 0, 0], [1, 1, 1, 1], 4);

figure;

freqz(b);