IIR Filters Design

Functions
int	dspl_ap2bpass (double *b, double *a, int n, double wp0, double wp1, double *beta, double *alpha)
	Analog low-pass prototype frequency transformation to a band-pass filter with [wp0 ... wp1] pass-band. More...
int	dspl_ap2bstop (double *b, double *a, int n, double ws0, double ws1, double *beta, double *alpha)
	Analog low-pass prototype frequency transformation to a band-stop filter with [wp0 ... wp1] stop-band. More...
int	dspl_ap2high (double *b, double *a, int n, double wp, double *beta, double *alpha)
	Analog low-pass prototype frequency transformation to a high-pass filter with wp cutoff. More...
int	dspl_ap2low (double *b, double *a, int n, double wp, double *beta, double *alpha)
	Analog low-pass prototype frequency transformation to a low-pass filter with wp cutoff. More...
int	dspl_butter_ap (double Rp, int ord, double *b, double *a)
	Analog Butterworth filter prototype. More...
int	dspl_cheby1_ap (double Rp, int ord, double *b, double *a)
	Analog Chebyshev type 1 filter prototype. More...
int	dspl_cheby2_ap (double Rs, int ord, double *b, double *a)
	Analog Chebyshev type 2 filter prototype. More...

Detailed Description

Functions for digital IIR filter design.

Function Documentation

dspl_ap2bpass()

int dspl_ap2bpass	(	double *	b,
		double *	a,
		int	n,
		double	wp0,
		double	wp1,
		double *	beta,
		double *	alpha
	)

Analog low-pass prototype frequency transformation to a band-pass filter with [wp0 ... wp1] pass-band.

Function transforms analog prototype filter transfer function \( H_{\text{ap}}(s) \) to a band-pass filter transfer function \( H(s) \):

\[ H(s) = H_{\text{ap}} \left(\frac{s^2 + w^2_0}{B \cdot s} \right), \]

here \(w^2_0 = \) wp0 * wp1, \(wB = \)wp1 - wp0.

Result band-pass filter order is 2*n.

Parameters

[in]	b	Analog prototype \( H_{\text{ap}}(s) \) numerator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	a	Analog prototype \( H_{\text{ap}}(s) \) denominator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	n	Analog prototype filter order
[in]	wp0	Band-pass low frequency (rad/s) after transformation
[in]	wp1	Band-pass hight frequency (rad/s) after transformation
[out]	beta	Analog band-pass filter \( H(s) \) numerator coefficients vector pointer after transformation. Vector size is [2n+1 x 1].
[out]	alpha	Analog band-pass filter \( H(s) \) denominator coefficients vector pointer after transformation. Vector size is [2n+1 x 1].

Returns

DSPL_OK if filter has been transformed successfully or code of error otherwise.

Author

Sergey Bakhurin. www.dsplib.org

dspl_ap2bstop()

int dspl_ap2bstop	(	double *	b,
		double *	a,
		int	n,
		double	wp0,
		double	wp1,
		double *	beta,
		double *	alpha
	)

Analog low-pass prototype frequency transformation to a band-stop filter with [wp0 ... wp1] stop-band.

Function transforms analog prototype filter transfer function \( H_{\text{ap}}(s) \) to a band-stop filter transfer function \( H(s) \):

\[ H(s) = H_{\text{ap}} \left(\frac{B \cdot s}{s^2 + w^2_0} \right), \]

here \(w^2_0 = \) wp0 * wp1, \(wB = \)wp1 - wp0.

Result band-stop filter order is 2*n.

Parameters

[in]	b	Analog prototype \( H_{\text{ap}}(s) \) numerator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	a	Analog prototype \( H_{\text{ap}}(s) \) denominator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	n	Analog prototype filter order
[in]	wp0	Band-stop low frequency (rad/s) after transformation
[in]	wp1	Band-stop hight frequency (rad/s) after transformation
[out]	beta	Analog band-stop filter \( H(s) \) numerator coefficients vector pointer after transformation. Vector size is [2n+1 x 1].
[out]	alpha	Analog band-stop filter \( H(s) \) denominator coefficients vector pointer after transformation. Vector size is [2n+1 x 1].

Returns

DSPL_OK if filter has been transformed successfully or code of error otherwise.

Author

Sergey Bakhurin. www.dsplib.org

dspl_ap2high()

int dspl_ap2high	(	double *	b,
		double *	a,
		int	n,
		double	wp,
		double *	beta,
		double *	alpha
	)

Analog low-pass prototype frequency transformation to a high-pass filter with wp cutoff.

Function transforms analog prototype filter transfer function \( H_{\text{ap}}(s) \) to a high-pass filter transfer function \( H(s) \):

\[ H(s) = H_{\text{ap}} \left(\frac{w_p}{s} \right), \]

Result high-pass filter order is n.

Parameters

[in]	b	Analog prototype \( H_{\text{ap}}(s) \) numerator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	a	Analog prototype \( H_{\text{ap}}(s) \) denominator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	n	Analog prototype filter order
[in]	wp	High-pass cutoff frequency (rad/s) after transformation
[out]	beta	Analog high-pass filter \( H(s) \) numerator coefficients vector pointer after transformation. Vector size is [n+1 x 1].
[out]	alpha	Analog high-pass filter \( H(s) \) denominator coefficients vector pointer after transformation. Vector size is [n+1 x 1].

Returns

DSPL_OK if filter has been transformed successfully or code of error otherwise.

Author

Sergey Bakhurin. www.dsplib.org

dspl_ap2low()

int dspl_ap2low	(	double *	b,
		double *	a,
		int	n,
		double	wp,
		double *	beta,
		double *	alpha
	)

Analog low-pass prototype frequency transformation to a low-pass filter with wp cutoff.

Function transforms analog prototype filter transfer function \( H_{\text{ap}}(s) \) to a low-pass filter transfer function \( H(s) \):

\[ H(s) = H_{\text{ap}} \left(\frac{s}{w_p} \right), \]

Result low-pass filter order is n.

Parameters

[in]	b	Analog prototype \( H_{\text{ap}}(s) \) numerator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	a	Analog prototype \( H_{\text{ap}}(s) \) denominator coefficients vector pointer. Vector size is [n+1 x 1].
[in]	n	Analog prototype filter order
[in]	wp	Low-pass cutoff frequency (rad/s) after transformation
[out]	beta	Analog low-pass filter \( H(s) \) numerator coefficients vector pointer after transformation. Vector size is [n+1 x 1].
[out]	alpha	Analog low-pass filter \( H(s) \) denominator coefficients vector pointer after transformation. Vector size is [n+1 x 1].

Returns

DSPL_OK if filter has been transformed successfully or code of error otherwise.

Author

Sergey Bakhurin. www.dsplib.org

dspl_butter_ap()

int dspl_butter_ap	(	double	Rp,
		int	ord,
		double *	b,
		double *	a
	)

Analog Butterworth filter prototype.

Function calculates Analog Butterworth filter transfer function \(H(s)\) coefficients. Filter has order ord cutoff frequency 1 rad/s with distortion level -Rp dB in passband (from 0 rad/s to 1 rad/s).

Parameters

[in]	Rp	Filter passband distortions dB. Distortions level from 0 rad/s to 1 rad/s. Must be positive.
[in]	ord	Filter order. Transfer function \(H(s)\) numerator and denominator coefficients number is ord+1.
[out]	b	Transfer function \(H(s)\) numerator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.
[out]	a	Transfer function \(H(s)\) denominator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.

Returns

DSPL_OK Filter is calculated successfully .
DSPL_ERROR_FILTER_RP Parameter Rp must be positive.
DSPL_ERROR_FILTER_ORD Filter order must be positive.
DSPL_ERROR_PTR Pointers b and a cannot be as NULL.

Author

Sergey Bakhurin. www.dsplib.org

dspl_cheby1_ap()

int dspl_cheby1_ap	(	double	Rp,
		int	ord,
		double *	b,
		double *	a
	)

Analog Chebyshev type 1 filter prototype.

Function calculates Analog Chebyshev type 1 filter transfer function \(H(s)\) coefficients. Filter has order ord cutoff frequency 1 rad/s with distortion level -Rp dB in passband (from 0 rad/s to 1 rad/s). Chebyshev type 1 filter magnitude is equiripple in passband.

Parameters

[in]	Rp	Filter passband distortions dB. Distortions level from 0 rad/s to 1 rad/s. Must be positive.
[in]	ord	Filter order. Transfer function \(H(s)\) numerator and denominator coefficients number is ord+1.
[out]	b	Transfer function \(H(s)\) numerator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.
[out]	a	Transfer function \(H(s)\) denominator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.

Returns

DSPL_OK Filter is calculated successfully .
DSPL_ERROR_FILTER_RP Parameter Rp must be positive.
DSPL_ERROR_FILTER_ORD Filter order must be positive.
DSPL_ERROR_PTR Pointers b and a cannot be as NULL.

Author

Sergey Bakhurin. www.dsplib.org

dspl_cheby2_ap()

int dspl_cheby2_ap	(	double	Rs,
		int	ord,
		double *	b,
		double *	a
	)

Analog Chebyshev type 2 filter prototype.

Function calculates Analog Chebyshev type 2 filter transfer function \(H(s)\) coefficients. Filter has order ord stopband frequency 1 rad/s with suppression level -Rs dB in stopband.

Parameters

[in]	Rs	Filter stopband suppression dB. Must be positive.
[in]	ord	Filter order. Transfer function \(H(s)\) numerator and denominator coefficients number is ord+1.
[out]	b	Transfer function \(H(s)\) numerator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.
[out]	a	Transfer function \(H(s)\) denominator coefficients vector pointer. Vector size is [ord+1 x 1]. Memory must be allocated.

Returns

DSPL_OK Filter is calculated successfully .
DSPL_ERROR_FILTER_RS Parameter Rs must be positive.
DSPL_ERROR_FILTER_ORD Filter order must be positive.
DSPL_ERROR_PTR Pointers b and a cannot be as NULL.

Author

Sergey Bakhurin. www.dsplib.org