Functions
int DSPL_API	filter_freq_resp (double b, double a, int ord, double w, int n, int flag, double mag, double phi, double tau)
	Magnitude, phase response and group delay vectors calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function. More...

int DSPL_API	freqs (double b, double a, int ord, double w, int n, complex_t h)
	Analog filter frequency response \( H(j \omega) \) calculation. More...

int DSPL_API	freqz (double b, double a, int ord, double w, int n, complex_t h)
	Function calculates the digital filter frequency response \( H \left(e^{j \omega} \right)\) corresponds to transfer function \(H(z)\). More...

int DSPL_API	group_delay (double pb, double pa, int ord, int flag, double w, int n, double tau)
	Group delay calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function. More...

int DSPL_API	phase_delay (double b, double a, int ord, int flag, double w, int n, double tau)
	Phase delay calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function. More...

Detailed Description

This group describes the algorithm for calculation parameters for analog and digital filters: Magnitude, phase response, groupdelay, impulse response and other.

Function Documentation

◆ filter_freq_resp()

int filter_freq_resp	(	double *	b,
		double *	a,
		int	ord,
		double *	w,
		int	n,
		int	flag,
		double *	mag,
		double *	phi,
		double *	tau
	)

Magnitude, phase response and group delay vectors calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function.

Parameters

[in]	b	Pointer to the \( H(s) \) or \(H(z)\) transfer function numerator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	a	Pointer to the \( H(s) \) or \(H(z)\) transfer function denominator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	ord	Filter order. Transfer function \( H(s) \) or \(H(z)\) numerator and denominator coefficients number equals `ord+1`.
[in]	w	Pointer to the angular frequency \( \omega \) (rad/s), which used for analog filter characteristics calculation (flag sets as `DSPL_FLAG_ANALOG`). For digital filter (flag sets as `DSPL_FLAG_DIGITAL`), parameter `w` describes normalized frequency of frequency response \( H \left(\mathrm{e}^{j\omega} \right) \). Digital filter frequency response is \( 2\pi \)-periodic function, and vector `w` advisable to set from 0 to \( \pi \), or from 0 to \( 2\pi \), or from \( -\pi \) to \( \pi \). Vector size is `[n x 1]`.
[in]	n	Size of frequency vector `w`.
[in]	flag	Binary flags to set calculation rules: DSPL_FLAG_ANALOG Coefficients corresponds to analog filter DSPL_FLAG_DIGITAL Coefficients corresponds to digital filter DSPL_FLAG_LOGMAG Calculate magnitude in logarithmic scale (in dB) DSPL_FLAG_UNWRAP Unwrap radian phases by adding multiples of 2*pi
[out]	mag	Pointer to the filter magnitude vector. Vector size is `[n x 1]`. If pointer is `NULL`, then magnitude will not calculted.
[out]	phi	Pointer to the phase response vector. Vector size is `[n x 1]`. If pointer is `NULL`, then phase response will not calculted.
[out]	tau	Pointer to the group delay vector. Vector size is `[n x 1]`. If pointer is `NULL`, then group delay will not calculted.

Returns: RES_OK if function is calculated successfully.
Else code error.

Example:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "dspl.h"
 
/* Filter order */
#define ORD  3
 
/* Frequency response vector size */
#define N    1000
 
 
int main(int argc, char* argv[])
{
    void* hdspl;    /* DSPL handle */
    void* hplot;    /* GNUPLOT handle */
 
    /* Load DSPL functions */
    hdspl = dspl_load();
 
    double a[ORD+1]; /* H(s) numerator     coefficients vector  */
    double b[ORD+1]; /* H(s) denominator coefficients vector    */
    double Rp = 1.0; /* Magnitude ripple from 0 to 1 rad/s      */
    double w[N];     /* Angular frequency (rad/s)               */
    double mag[N];   /* Filter Magnitude (dB)                   */
    double phi[N];   /* Phase response                          */
    double tau[N];   /* Group delay                             */
 
 
    int k;
 
    /* H(s) coefficients calculation */
    int res = butter_ap(Rp, ORD, b, a);
    if(res != RES_OK)
        printf("error code = 0x%8x\n", res);
 
    /* Print H(s) coefficients */
    for(k = 0; k < ORD+1; k++)
        printf("b[%2d] = %9.3f         a[%2d] = %9.3f\n", k, b[k], k, a[k]);
 
    /* Frequency in logarithmic scale from 0.01 to 100 rad/s */
    logspace(-2.0, 2.0, N , DSPL_SYMMETRIC, w);
 
    /* Filter frequency parameter calculation */
    filter_freq_resp(b, a, ORD, w, N,
                     DSPL_FLAG_LOGMAG|DSPL_FLAG_UNWRAP|DSPL_FLAG_ANALOG,
                     mag, phi, tau);
 
    /* Write Magnitude, phase response and group delay to the files */
    writetxt(w, mag, N, "dat/butter_ap_test_mag.txt");
    writetxt(w, phi, N, "dat/butter_ap_test_phi.txt");
    writetxt(w, tau, N, "dat/butter_ap_test_tau.txt");
 
    /* plotting by GNUPLOT */
    gnuplot_create(argc, argv, 920, 260, "img/butter_ap_test.png", &hplot);
    gnuplot_cmd(hplot, "set logscale x");
    gnuplot_cmd(hplot, "unset key");
    gnuplot_cmd(hplot, "set grid");
    gnuplot_cmd(hplot, "set xlabel 'frequency, rad/s'");
    gnuplot_cmd(hplot, "set multiplot layout 1,3 rowsfirst");
    gnuplot_cmd(hplot, "set ylabel 'Magnitude, dB'");
    gnuplot_cmd(hplot, "set yrange [-100:5]");
    gnuplot_cmd(hplot, "plot 'dat/butter_ap_test_mag.txt' with lines");
    gnuplot_cmd(hplot, "set ylabel 'Phase response, rad'");
    gnuplot_cmd(hplot, "unset yrange");
    gnuplot_cmd(hplot, "plot 'dat/butter_ap_test_phi.txt' with lines");
    gnuplot_cmd(hplot, "set ylabel 'Groupdelay, sec'");
    gnuplot_cmd(hplot, "unset yrange");
    gnuplot_cmd(hplot, "plot 'dat/butter_ap_test_tau.txt' with lines");
    gnuplot_cmd(hplot, "unset multiplot");
    gnuplot_close(hplot);
 
    /* free dspl handle */
    dspl_free(hdspl);
 
    return res;
}
 

Result:

b[ 0] =   1.002   a[ 0] =   1.002
b[ 1] =   0.000   a[ 1] =   2.618
b[ 2] =   0.000   a[ 2] =   3.418
b[ 3] =   0.000   a[ 3] =   2.615
b[ 4] =   0.000   a[ 4] =   1.000

In dat folder will be created 3 files:

butter_ap_test_mag.txt    magnitude
butter_ap_test_phi.txt    phase response
butter_ap_test_tau.txt    group delay

In addition, GNUPLOT will build the following graphs from data stored in files:

Author: Sergey Bakhurin www.dsplib.org

Definition at line 235 of file filter_freq_resp.c.

Referenced by phase_delay().

◆ freqs()

int freqs	(	double *	b,
		double *	a,
		int	ord,
		double *	w,
		int	n,
		complex_t *	h
	)

Analog filter frequency response \( H(j \omega) \) calculation.

Function calculates analog filter frequency response \( H(j \omega)\) corresponds to transfer function \( H(s) \):

\[ H(s) = \frac {\sum_{k = 0}^{N} b_k s^k} {\sum_{m = 0}^{N} a_m s^m}, \]

here \( N \) - filter order (equals to ord).

Parameters

[in]	b	Pointer to the transfer function \( H(s) \) numerator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	a	Pointer to the transfer function \( H(s) \) denominator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	ord	Filter order. Transfer function \( H(s) \) numerator and denominator coefficients number equals `ord+1`.
[in]	w	Pointer to the angular frequency \( \omega \) (rad/s), which used for frequency response \( H(j \omega) \) calculation. Vector size is `[n x 1]`.
[in]	n	The size of the angular frequency vector `w`.
[out]	h	Pointer to the frequency response vector \( H(j \omega) \), corresponds to angular frequency `w`. Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if frequency response vector is calculated successfully.
Else code error.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 143 of file freqs.c.

Referenced by filter_freq_resp().

◆ freqz()

int freqz	(	double *	b,
		double *	a,
		int	ord,
		double *	w,
		int	n,
		complex_t *	h
	)

Function calculates the digital filter frequency response \( H \left(e^{j \omega} \right)\) corresponds to transfer function \(H(z)\).

Digital filter transfer function:

\[ H(z) = \frac{\sum\limits_{k = 0}^{N} b_k z^{-k}} {\sum\limits_{m = 0}^{N} a_m z^{-m}}, \]

here \(N\) — filter order (parameter ord).
Frequency response \( H \left(e^{j \omega} \right)\) we can get if substitute \(z = e^{j \omega} \).

Parameters

[in]	b	Pointer to the \( H(z) \) transfer function numerator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	a	Pointer to the \(H(z)\) transfer function denominator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	ord	Filter order. Transfer function \(H(z)\) numerator and denominator coefficients number equals `ord+1`.
[in]	w	Pointer to the normalized frequency of digital filter frequency response \( H \left(\mathrm{e}^{j\omega} \right) \). Digital filter frequency response is \( 2\pi \)-periodic function, and vector `w` advisable to set from 0 to \( \pi \), or from 0 to \( 2\pi \), or from \( -\pi \) to \( \pi \). Vector size is `[n x 1]`.
[in]	n	Size of frequency vector `w`.
[out]	h	Pointer to the frequency response vector \( H \left(\mathrm{e}^{j\omega} \right) \), corresponds to normalized frequency `w`. Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if frequency response vector is calculated successfully.
Else code error.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 157 of file freqz.c.

Referenced by filter_freq_resp().

◆ group_delay()

int DSPL_API group_delay	(	double *	b,
		double *	a,
		int	ord,
		int	flag,
		double *	w,
		int	n,
		double *	tau
	)

Group delay calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function.

Group delay is describes as:

\[ \tau_g(\omega) = - \frac{d\Phi(\omega)}{d\omega}, \]

here \(\Phi(\omega)\) – filter phase response, \(\omega\) is angular frequency for analog filter, or normalized frequency for digital filter.

Parameters

[in]	b	Pointer to the \( H(s) \) or \(H(z)\) transfer function numerator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	a	Pointer to the \( H(s) \) or \(H(z)\) transfer function denominator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	ord	Filter order. Transfer function \( H(s) \) or \(H(z)\) numerator and denominator coefficients number equals `ord+1`.
[in]	flag	Binary flags to set calculation rules: DSPL_FLAG_ANALOG Coefficients corresponds to analog filter DSPL_FLAG_DIGITAL Coefficients corresponds to digital filter
[in]	w	Pointer to the angular frequency \( \omega \) (rad/s), which used for analog filter characteristics calculation (flag sets as `DSPL_FLAG_ANALOG`). For digital filter (flag sets as `DSPL_FLAG_DIGITAL`), parameter `w` describes normalized frequency of frequency response \( H \left(\mathrm{e}^{j\omega} \right) \). Digital filter frequency response is \( 2\pi \)-periodic function, and vector `w` advisable to set from 0 to \( \pi \), or from 0 to \( 2\pi \), or from \( -\pi \) to \( \pi \). Vector size is `[n x 1]`.
[in]	n	Size of frequency vector `w`.
[out]	tau	Pointer to the group delay vector. Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if function is calculated successfully.
Else code error.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 164 of file group_delay.c.

Referenced by filter_freq_resp().

◆ phase_delay()

int DSPL_API phase_delay	(	double *	b,
		double *	a,
		int	ord,
		int	flag,
		double *	w,
		int	n,
		double *	tau
	)

Phase delay calculation for digital or analog filter corresponds to \(H(s)\), or \(H(z)\) transfer function.

Group delay is describes as:

\[ \tau_{\varphi}(\omega) = - \frac{\Phi(\omega)}{\omega}, \]

here \(\Phi(\omega)\) – filter phase response, \(\omega\) is angular frequency for analog filter, or normalized frequency for digital filter.

Parameters

[in]	b	Pointer to the \( H(s) \) or \(H(z)\) transfer function numerator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	a	Pointer to the \( H(s) \) or \(H(z)\) transfer function denominator coefficients vector. Vector size is `[ord+1 x 1]`.
[in]	ord	Filter order. Transfer function \( H(s) \) or \(H(z)\) numerator and denominator coefficients number equals `ord+1`.
[in]	flag	Binary flags to set calculation rules: DSPL_FLAG_ANALOG Coefficients corresponds to analog filter DSPL_FLAG_DIGITAL Coefficients corresponds to digital filter
[in]	w	Pointer to the angular frequency \( \omega \) (rad/s), which used for analog filter characteristics calculation (flag sets as `DSPL_FLAG_ANALOG`). For digital filter (flag sets as `DSPL_FLAG_DIGITAL`), parameter `w` describes normalized frequency of frequency response \( H \left(\mathrm{e}^{j\omega} \right) \). Digital filter frequency response is \( 2\pi \)-periodic function, and vector `w` advisable to set from 0 to \( \pi \), or from 0 to \( 2\pi \), or from \( -\pi \) to \( \pi \). Vector size is `[n x 1]`.
[in]	n	Size of frequency vector `w`.
[out]	tau	Pointer to the phase delay vector. Vector size is `[n x 1]`. Memory must be allocated.

Returns: RES_OK if function is calculated successfully.
Else code error.

Author: Sergey Bakhurin www.dsplib.org

Definition at line 165 of file phase_delay.c.

Functions

Detailed Description

Function Documentation

◆ filter_freq_resp()

◆ freqs()

◆ freqz()

◆ group_delay()

◆ phase_delay()