Basic functions of real and complex arguments.

Functions
int	dspl_linspace (double x0, double x1, int n, int type, double *x)
	Linspace filling of the array x from x0 to x1 More...
int	dspl_log_cmplx (double *xR, double *xI, int n, double *yR, double *yI)
	Logarithm of complex arguments. More...
int	dspl_logspace (double x0, double x1, int n, int type, double *x)
	Logspace filling of the array x from 10^x0 to 10^x1 More...
int	dspl_polyval (double *a, int ord, double *x, int n, double *y)
	Real polynomial calculation. More...
int	dspl_polyval_cmplx (double *aR, double *aI, int ord, double *xR, double *xI, int n, double *yR, double *yI)
	Complex values polynomial calculation. More...
int	dspl_sqrt_cmplx (double *xR, double *xI, int n, double *yR, double *yI)
	Square root of complex arguments. More...
int	dspl_unwrap (double *phi, int n, double lev, double mar)
	Раскрытие периодичности арктангенса при расчете фазо-частотной характеристики. More...

Detailed Description

Function Documentation

dspl_linspace()

int dspl_linspace	(	double	x0,
		double	x1,
		int	n,
		int	type,
		double *	x
	)

Linspace filling of the array x from x0 to x1

Function supports two kind of filling according to parameter type:

Symmetric filling corresponds to equation

\(x(k) = x_0 + k \cdot dx\), here \(dx = \frac{x_1 - x_0}{n-1}\), \(k = 0 \ldots n-1.\)

Periodic filling corresponds to equation

\(x(k) = x_0 + k \cdot dx\), here \(dx = \frac{x_1 - x_0}{n}\), \(k = 0 \ldots n-1.\)

Parameters

[in]	x0	Initial value \(x_0\).
[in]	x1	Stop value \(x_1\).
[in]	n	Array x number of points.
[in]	type	Filling type DSPL_SYMMETRIC - symmetric filling, DSPL_PERIODIC - periodic filling.
[in,out]	x	Linspace array pointer. Vector size is [n x 1]. Memory must be allocated.

Returns

DSPL_OK - Function has been finished successfully .
DSPL_ERROR_PTR - pointer x cannot be NULL.
DSPL_ERROR_SIZE - Vector x size must be more than 1.

Note

We can understand a difference between periodic and a symmetric types from the examples below.
Example 1. Periodic filling.

double x[5];
dspl_linspace(0, 5, 5, DSPL_PERIODIC, x);

Vector x will keep follow values:

0, 1, 2, 3, 4

Examples 2. Symmetric filling.

double x[5];
dspl_linspace(0, 5, 5, DSPL_SYMMETRIC, x);

Vector x will keep follow values:

0, 1.25, 2.5, 3.75, 5

Author

Sergey Bakhurin. www.dsplib.org

Examples:

hilbert_fft.c, resample_lagrange_ex_interp.c, resample_lagrange_filter_frac_delay.c, resample_lagrange_filter_interp.c, resample_spline_ex_interp.c, resample_spline_filter_frac_delay.c, and resample_spline_filter_interp.c.

dspl_log_cmplx()

int dspl_log_cmplx	(	double *	xR,
		double *	xI,
		int	n,
		double *	yR,
		double *	yI
	)

Logarithm of complex arguments.

Function calculates logarithm function of a complex vector argument \( x \).

\[ \ln(x) = \ln \left( |x| \right) + j \cdot \arg(x). \]

Parameters

[in]	xR	Pointer to the complex vector \( x \) real part. Vector size is [n x 1].
[in]	xI	Pointer to the complex vector \( x \) image part. Vector size is [n x 1]. This pointer can be a NULL if function uses real argument only.
[in]	n	Input vector size.
[out]	yR	Pointer to the logarithm real part values. Vector size is [n x 1]. Memory must be allocated.
[out]	yI	Pointer to the logarithm image part values. Vector size is [n x 1]. Memory must be allocated (even if xI is NULL).

Returns

DSPL_OK if complex logarithm has been calculated successfully, else error code.

Author

Sergey Bakhurin. www.dsplib.org

dspl_logspace()

int dspl_logspace	(	double	x0,
		double	x1,
		int	n,
		int	type,
		double *	x
	)

Logspace filling of the array x from 10^x0 to 10^x1

Function supports two kind of filling according to parameter type:

Symmetric filling corresponds to equation

\(x(k) = 10^{x_0} \cdot dx^k\), где \(dx = \sqrt[n-1]{10^{x_1 - x_0}}\), \(k = 0 \ldots n-1.\)

Periodic filling corresponds to equation

\(x(k) = 10^{x_0} \cdot dx^k\), где \(dx = \sqrt[n]{10^{x_1 - x_0}}\), \(k = 0 \ldots n-1.\)

Parameters

[in]	x0	Initial value \(x_0\).
[in]	x1	Stop value \(x_1\).
[in]	n	Array x number of points.
[in]	type	Filling type DSPL_SYMMETRIC - symmetric filling, DSPL_PERIODIC - periodic filling.
[in,out]	x	Logspace array pointer. Vector size is [n x 1]. Memory must be allocated.

Returns

DSPL_OK - Function has been finished successfully .
DSPL_ERROR_PTR - pointer x cannot be NULL.
DSPL_ERROR_SIZE - Vector x size must be more than 1.

Note

We can understand a difference between periodic and a symmetric types from the examples below.
Example 1. Periodic filling.

double x[5];
dspl_logspace(-2, 3, 5, DSPL_PERIODIC, x);

Vector x will keep follow values:

0.01, 0.1, 1, 10, 100

Examples 2. Symmetric filling.

double x[5];
dspl_logspace(-2, 3, 5, DSPL_SYMMETRIC, x);

Vector x will keep follow values:

0.01 0.178 3.162 56.234 1000

Author

Sergey Bakhurin. www.dsplib.org

dspl_polyval()

int dspl_polyval	(	double *	a,
		int	ord,
		double *	x,
		int	n,
		double *	y
	)

Real polynomial calculation.

Function calculates a \(N-\) th order polynomial \(P_N(x)\)

\[ P_N(x) = a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3*x^3 + ... a_N*x^N. \]

for vector argument x. Output is vector y which contains polynomial values for each x This function uses Horner's polynomial factorization:

\[ P_N(x) = a_0 + x \cdot (a_1 + x \cdot (a_2 + \cdot ( \ldots x \cdot (a_{N-1} + x\cdot a_N) \ldots ))) \]

Parameters

[in]	a	Polynomial coefficients vector pointer. Vector size is [ord+1 x 1]. Coefficient a[0] corresponds to \(a_0\) polynomial coefficient
[in]	ord	Polynomial order \(N\).
[in]	x	Polynomial argument vector pointer. Vector size is [n x 1]. Polynomial will be calculated for all x values.
[in]	n	Polynomial argument vector size.
[out]	y	Polynomial values for all arguments x. Vector size is [n x 1] Memory must be allocated.

Returns

DSPL_OK Polynomial is calculated successfully.
DSPL_ERROR_PTR Pointers a, x and y cannot to be as NULL.
DSPL_ERROR_SIZE Argument vector size is wrong (n < 1).
DSPL_ERROR_POLY_ORD Polynomial order less than 0.

Author

Sergey Bakhurin. www.dsplib.org

Examples:

resample_lagrange_ex_frac_delay.c, and resample_spline_ex_frac_delay.c.

dspl_polyval_cmplx()

int dspl_polyval_cmplx	(	double *	aR,
		double *	aI,
		int	ord,
		double *	xR,
		double *	xI,
		int	n,
		double *	yR,
		double *	yI
	)

Complex values polynomial calculation.

Function calculates a \(N-\) th order polynomial \(P_N(x)\)

\[ P_N(x) = a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3*x^3 + ... a_N*x^N. \]

for vector argument x. Output is vector y which contains polynomial values for each x This function uses Horner's polynomial factorization:

\[ P_N(x) = a_0 + x \cdot (a_1 + x \cdot (a_2 + \cdot ( \ldots x \cdot (a_{N-1} + x\cdot a_N) \ldots ))) \]

Parameters

[in]	aR	Polynomial coefficients real part vector pointer. Vector size is [ord+1 x 1]. Coefficient a[0] corresponds to \(a_0\) polynomial coefficient
[in]	aI	Polynomial coefficients image part vector pointer. Vector size is [ord+1 x 1]. Coefficient a[0] corresponds to \(a_0\) polynomial coefficient
[in]	ord	Polynomial order \(N\).
[in]	xR	Polynomial argument real part vector pointer. Vector size is [n x 1]. Polynomial will be calculated for all x values.
[in]	xI	Polynomial argument image part vector pointer. Vector size is [n x 1]. Polynomial will be calculated for all x values.
[in]	n	Polynomial argument vector size.
[out]	yR	Polynomial real part values for all arguments x. Vector size is [n x 1] Memory must be allocated.
[out]	yI	Polynomial image part values for all arguments x. Vector size is [n x 1] Memory must be allocated.

Returns

DSPL_OK Polynomial is calculated successfully.
DSPL_ERROR_PTR Pointers aR, xR and yR cannot to be as NULL.
Pointer yI can be NULL only if aI and xI are NULL. DSPL_ERROR_SIZE Argument vector size is wrong (n < 1).
DSPL_ERROR_POLY_ORD Polynomial order less than 0.

Author

Sergey Bakhurin. www.dsplib.org

dspl_sqrt_cmplx()

int dspl_sqrt_cmplx	(	double *	xR,
		double *	xI,
		int	n,
		double *	yR,
		double *	yI
	)

Square root of complex arguments.

Function calculates square root function of a complex vector argument \( x \).

\[ \sqrt {x}={\sqrt {\frac {|x|+\Re (x)}{2}}} + \operatorname {sign} \left(\Im (x) \right) \cdot j\ {\sqrt {\frac {|x|-\Re (x)}{2}}}. \]

Parameters

[in]	xR	Pointer to the complex vector \( x \) real part. Vector size is [n x 1].
[in]	xI	Pointer to the complex vector \( x \) image part. Vector size is [n x 1]. This pointer can be a NULL if function uses real argument only.
[in]	n	Input vector size.
[out]	yR	Pointer to the square root real part values. Vector size is [n x 1]. Memory must be allocated.
[out]	yI	Pointer to the square root image part values. Vector size is [n x 1]. Memory must be allocated (even if xI is NULL).

Returns

DSPL_OK if complex square root has been calculated successfully, else error code.

Author

Sergey Bakhurin. www.dsplib.org

dspl_unwrap()

int dspl_unwrap	(	double *	phi,
		int	n,
		double	lev,
		double	mar
	)

Раскрытие периодичности арктангенса при расчете фазо-частотной характеристики.

Parameters

[in,out]	phi	Указатель на вектор фазо-частотной характеристики. Размер вектора [n x 1]. ФЧХ после раскрытия будет помещена по этому же адресу.
[in]	n	Размер вектора ФЧХ.
[in]	lev	Период арктангенса. M_2PI или M_PI в зависимости от способа расчета ФЧХ. Так при использовании функции atan периодичность составит M_PI, а при использовании atan2 периодичность равна M_2PI.
[in]	mar	Запас при котором считается, что произошел переход на следующий период арктангенса. Значение от 0 до 1. Так например если lev = M_PI и mar = 0.8, то переход на следующий период арктангенса будет зафиксирован если |p[k] - phi[k-1]| > 0.8 * M_PI.

Author

Бахурин Сергей. www.dsplib.org

Note

Данная функция является рекурсивной. Это означает что она выполняется до тех пор пока в исходном векторе будут определены переходы на следующий период арктангенса.
Так например функция работает корректно если в исходной фазо-частотной характеристике период фазы составляет \( 2\pi \), в то время как lev = M_PI. Функция осуществит два прохода в этом случае и корректно раскроет периодичность по фазе.