2.1.22.3.8 ocmsp_iir_filter_sos

Description

Design digital or analog IIR filters with given specifications. It returns a filter in second-order section representation:

\[ H(z) = g \prod_{k=0}^{L-1} {H_{k(z)}} = g \prod_{k=0}^{L-1} \frac{b_{0k}+b_{1k}*z^{-1}+b_{2k}*z^{-2}}{1+a_{1k}*z^{-1}+a_{2k}*z^{-2}} \]

The result is saved in an L-by-6 matrix sos, and a scalar gain.

\[ sos = \begin{vmatrix} b_{01} & b_{11} & b_{21} & 1 & a_{11} & a_{21} \\ b_{02} & b_{12} & b_{22} & 1 & a_{12} & a_{22} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ b_{0L} & b_{1L} & b_{2L} & 1 & a_{1L} & a_{2L} \end{vmatrix} \]

Each row in sos is the numerator and denominator coefficients \(b_{ik}\) and \(a_{ik}\) of the second order sections of H(z). Section number L is the closest integer greater than or equal to n/2 (L = (n+1)/2).

Syntax

int ocmsp_iir_filter_sos( UINT N, double Wn, double * pSOS, double * pg, int type, double Rp = 0.0, double Rs = 0.0, double Wn2 = -1.0 )

Parameters

N

[input] filter order, should be even if is bandpass or bandstop type

Wn

[input] cutoff or passband/stopband-edge frequency, it's in radians/s if is analog type, and should be normalized to [0, 1] if is digital type, where 1 corresponds to half the sample rate

pSOS

[output] coefficients matrix of second-order sections H(z), size nsec-by-6, nsec = (N+1)/2

pg

[output] returned gain, scalar

type

[intput] filter type, it specifies the filter prototype(Butterworth, Chebyshev Type I, Chebyshev Type II, Elliptic or Bessel), bandtype(lowpass, highpass, bandstop or bandpass) and digital or analog type. For example

OMSP_BUTTERWORTH|OMSP_LOWPASS|OMSP_DIGITAL means a lowpass Butterworth digital filter.

Rp

[input][optional] passband ripple (dB), needed when it's Chebyshev Type I or Elliptic type

Rs

[input][optional] stopband attenuation (dB), needed when it's Chebyshev Type II or Elliptic type

Wn2

[input][optional] cutoff or passband/stopband-edge frequency. Needed when it's a bandpass or bandstop

filter. It's in radians/second if is analog type, and should be normalized to [0, 1] if is digital type (where 1 corresponds to half the sample rate).

Return

Return OE_NOERROR if succeed, otherwise, non-zero error code is returned (OE_NULL_POINTER, OE_INVALID_FREQ, OE_INVALID_BANDFREQS, OE_INVLAID_RIPPLE, OE_INVALID_BANDRIPPLES or OE_INVALID_TYPE)

Examples

EX1

#include <ocmsp.h>
void ocmsp_iir_filter_sos_ex1()
{
    UINT N = 18; //even number if bandpass or bandstop
    double Wn[2] = {300.0/500, 400.0/500};

    UINT nsec = (N+1)/2; //size L = (n+1)/2;
    matrix sos(nsec, 6);
    double gain;
    int type = OMSP_BUTTERWORTH|OMSP_BANDPASS|OMSP_DIGITAL;

    int nRet = 0;
    if (0 != (nRet = ocmsp_iir_filter_sos(N, Wn[0], sos, &gain, type, 0.0, 0.0, Wn[1])))
    {
        printf("ocmsp_iir_filter_sos failed, error code=%d\n", nRet);
        return;
    }
}

Remark

See Also

ocmsp_iir_filter, ocmsp_iir_filter_ss, ocmsp_iir_filter_zp

Header to Included

ocmsp.h

Reference