Finite Impulse Response (FIR) Design using Parks-McClellan Algorithm

FIR filter design using the Parks-McClellan algorithm is implemented in liquid with the firdespm interface. The Parks-McClellan algorithm uses the Remez exchange algorithm to solve the minimax problem (minimize the maximum error) for filter design. The interface accepts a description of \(N_b\) disjoint and non-overlapping frequency bands with a desired response and relative error weighting for each, and computes the resulting filter coefficients.

int firdespm_run(unsigned int            _h_len,
                 unsigned int            _num_bands,
                 float *                 _bands,
                 float *                 _des,
                 float *                 _weights,
                 liquid_firdespm_wtype * _wtype,
                 liquid_firdespm_btype   _btype,
                 float *                 _h);

• _bands is a \([N_b \times 2]\) matrix of the band edge descriptions. Each row corresponds to an upper and lower band edge for each region of interest. These regions cannot be overlapping.

• _des is an array of size \(N_b\) with the desired response (linear) for each band.

• _weights is an array of size \(N_b\) with the relative error weighting for each band.

• _num_bands represents \(N_b\), the number of bands in the design.

• _btype gives the filter type for the design. This is typically LIQUID_FIRDESPM_BANDPASS for the majority of filters.

• _wtype is an array of length \(N_b\) which specifies the weighting function for each band (flat, exponential, or linear).

Example

Listed below is an example of the firdespm interface.

#include <stdio.h>
#include <stdlib.h>
#include "liquid.h"

int main(int argc, char*argv[]) {
    // options
    unsigned int          n     = 101;  // filter length
    liquid_firdespm_btype btype = LIQUID_FIRDESPM_BANDPASS;
    unsigned int num_bands = 4;
    float bands[8]   = {0.00f,  0.10f,  // 1
                        0.12f,  0.29f,  // 0
                        0.30f,  0.40f,  // 0.1
                        0.41f,  0.50f}; // 0
    float des[4]     = {1.0f, 0.0f, 0.1f, 0.0f};
    float weights[4] = {1.0f, 1.0f, 1.0f, 1.0f};

    liquid_firdespm_wtype wtype[4] = {LIQUID_FIRDESPM_FLATWEIGHT,
                                      LIQUID_FIRDESPM_FLATWEIGHT,
                                      LIQUID_FIRDESPM_FLATWEIGHT,
                                      LIQUID_FIRDESPM_FLATWEIGHT};
    float h[n];
    firdespm_run(n,num_bands,bands,des,weights,wtype,btype,h);

    printf("w\n");
    unsigned int i;
    for (i=0; i<n; i++)
        printf("%12.8f\n",h[i]);

    return 0;
}

Figure 6 Example of firdespm