Math statistic functions.

Functions
int DSPL_API	xcorr_cmplx (complex_t *x, int nx, complex_t *y, int ny, int flag, int nr, complex_t *r, double *t)
	Estimates the cross-correlation vector for complex discrete-time sequences x and y. More...
int DSPL_API	find_max_abs (double *a, int n, double *m, int *ind)
	Find maximum absolute value from the real vector a More...
int DSPL_API	mean (double *x, int n, double *m)
	Calculates the mean of the input vector x More...
int DSPL_API	mean_cmplx (complex_t *x, int n, complex_t *m)
	Calculates the mean of the complex input vector x More...
int DSPL_API	stat_std (double *x, int n, double *s)
	Calculates the standard deviation of the input vector x More...
int DSPL_API	stat_std_cmplx (complex_t *x, int n, double *s)
	Calculates the standard deviation of the complex input vector x More...
int DSPL_API	xcorr (double *x, int nx, double *y, int ny, int flag, int nr, double *r, double *t)
	Estimates the cross-correlation vector for real discrete-time sequences x and y. More...

Detailed Description

Function Documentation

find_max_abs()

int find_max_abs	(	double *	a,
		int	n,
		double *	m,
		int *	ind
	)

Find maximum absolute value from the real vector a

---

Function searches maximum absolute value in the real vector a. This value writes to the address m and index keeps to te address ind.

Parameters

[in]	a	Pointer to the real vector a. Vector size is [n x 1].
[in]	n	Size of the input vector a.
[out]	m	Pointer to the variable which keeps vector a maximum absolute value. Pointer can be NULL, maximum value will not return in this case.
[out]	ind	Pointer to the variable which keeps index of a maximum absolute value inside vector a. Pointer can be NULL, index will not return in this case.

Returns

RES_OK if function calculates successfully, else code error.

Example:

double a[5] = {0.0, 2.0, -5.0, 4.0, 2.0};
double m;
int ind;
find_max_abs(a, 5, &m, &ind);
printf("\n\nmax absolute value:        %8.1f    (index %d)", m, ind);

As result the variable m will keep value 5, and variable ind will keep 2.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 121 of file find_max_abs.c.

mean()

int mean	(	double *	x,
		int	n,
		double *	m
	)

Calculates the mean of the input vector x

---

Function calculates the mean value

\[ m = \frac{1}{n}\sum_{i = 0}^{n-1} x(i) \]

Parameters

[in]	x	Pointer to the real input vector x. Vector size is [n x 1].
[in]	n	Size of input vector x.
[out]	m	Pointer to the variable which keeps vector x mean value. Memory must be allocated. RES_OK if function calculates successfully, else code error.

Example:

double a[5] = {0.0, 1.0, 2.0, 3.0, 4.0};
double m;
mean(a, 5, &m);
printf("\n\n Mean value:    %8.1f\n", m);

As result the variable m will keep value 2.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 105 of file mean.c.

Referenced by stat_std().

mean_cmplx()

int mean_cmplx	(	complex_t *	x,
		int	n,
		complex_t *	m
	)

Calculates the mean of the complex input vector x

---

Function calculates the mean value

\[ m = \frac{1}{n}\sum_{i = 0}^{n-1} x(i) \]

Parameters

[in]	x	Pointer to the complex input vector x. Vector size is [n x 1].
[in]	n	Size of input vector x.
[out]	m	Pointer to the variable which keeps vector x mean value. Memory must be allocated. RES_OK if function calculates successfully, else code error.

Example:

complex_t a[3] = {{0.0, -1.0}, {1.0, 2.0}, {3.0, 5.0}};
complex_t m;
mean_cmplx(a, 3, &m);
printf("\n\n Mean value:    %8.1f%+3.1fj\n", RE(m), IM(m));

As result the variable m will keep value 1 + 3j.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 108 of file mean_cmplx.c.

Referenced by stat_std_cmplx().

stat_std()

int stat_std	(	double *	x,
		int	n,
		double *	s
	)

Calculates the standard deviation of the input vector x

---

Function calculates the the standard deviation value

\[ s = \sqrt{\frac{1}{n-1} \sum_{i = 0}^{n-1} \big(x(i) - \mu \big)^2}, \]

here \(\mu\) - mean value of the vector x:

\[ \mu = \frac{1}{n} \sum_{i = 0}^{n-1} x(i). \]

Parameters

[in]	x	Pointer to the real input vector x. Vector size is [n x 1].
[in]	n	Size of input vector x.
[out]	s	Pointer to the variable which keeps vector x standard deviation value. Memory must be allocated. RES_OK if function calculates successfully, else code error.

Example:

double a[5] = {0.0, 1.0, 2.0, 3.0, 4.0};
double s;
stat_std(a, 5, &s);
printf("\n\n Standard deviation value:    %8.1f\n", s);

As result the variable s will keep value 1.5811.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 116 of file stat_std.c.

stat_std_cmplx()

int stat_std_cmplx	(	complex_t *	x,
		int	n,
		double *	s
	)

Calculates the standard deviation of the complex input vector x

---

Function calculates the the standard deviation value

\[ s = \sqrt{\frac{1}{n-1} \sum_{i = 0}^{n-1} \big|x(i) - \mu \big|^2}, \]

here \(\mu\) - mean value of the vector x:

\[ \mu = \frac{1}{n} \sum_{i = 0}^{n-1} x(i). \]

Parameters

[in]	x	Pointer to the complex input vector x. Vector size is [n x 1].
[in]	n	Size of input vector x.
[out]	s	Pointer to the variable which keeps vector x standard deviation value. Memory must be allocated. RES_OK if function calculates successfully, else code error.

Example:

complex_t a[3] = {{0.0, -1.0}, {1.0, 2.0}, {3.0, 5.0}};
double s;
stat_std_cmplx(a, 3, &s);
printf("\n\n Standard deviation value:    %8.1f\n", s);

As result the variable s will keep value 3.3665.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 113 of file stat_std_cmplx.c.

xcorr()

int xcorr	(	double *	x,
		int	nx,
		double *	y,
		int	ny,
		int	flag,
		int	nr,
		double *	r,
		double *	t
	)

Estimates the cross-correlation vector for real discrete-time sequences x and y.

---

Estimate the cross correlation \(\widehat{r}_{xy}(k)\) of vector arguments x and y or estimate autocorrelation vector if \(x = y \).

Cross-correlation vector is defined as:

\[ \widehat{r}_{xy}(k) = \frac{1}{N-k} \sum\limits_{n = 0}^{N-k-1} x(n+k)y^*(n), \qquad 0 \leq k <N; \]

\[ \widehat{r}_{xy}(k) = \frac{1}{N+k} \sum\limits_{n = 0}^{N+k-1} y^*(n-k)x(n), \qquad -N < k < 0. \]

here \( N = \max(n_x, n_y) \).

This function uses the FFT algorithm to estimate the scaled correlation vector:

\[ \breve{r}_{xy}(k) = \operatorname{IFFT}\Big[ \operatorname{FFT}\big[ \mathbf{x} \big] \operatorname{FFT}^*\big[ \mathbf{y} \big] \Big] \]

Parameters

[in]	x	Pointer to the discrete-time vector x. Vector size is [nx x 1].
[in]	nx	Size of vector x.
[in]	y	Pointer to the discrete-time vector y. Vector size is [ny x 1].
[in]	ny	Size of vector y.
[in]	flag	Flag specifies the type of scaling applied to the correlation vector \(\breve{r}_{xy}(k)\). Is one of: DSPL_XCORR_NOSCALE unscaled correlation vector from IFFT output \(\breve{r}_{xy}(k)\); DSPL_XCORR_BIASED biased correlation vector \(\breve{r}_{xy}(k)/N \); DSPL_XCORR_UNBIASED unbiased correlation vector \(\widehat{r}_{xy}(k) = \frac{\breve{r}_{xy}(k)}{N-|k|} \);
[in]	nr	Maximum correlation lag. Correlation vector \(\widehat{r}_{xy}(k)\) is calculated for \( k= -n_r,\,\, -n_r +1, \ldots n_r\).
[out]	r	Pointer to the cross-correlation or autocorrelation vector. Vector size is [(2*nr+1) x 1]. Memory must be allocated.
[out]	r	Pointer to the cross-correlation argument vector \( k= -n_r,\,\, -n_r +1, \ldors n_r\). Vector size is [(2*nr+1) x 1]. Pointer can be NULL.

Returns

RES_OK if function returns successfully.
Else code error.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 214 of file xcorr.c.

xcorr_cmplx()

int DSPL_API xcorr_cmplx	(	complex_t *	x,
		int	nx,
		complex_t *	y,
		int	ny,
		int	flag,
		int	nr,
		complex_t *	r,
		double *	t
	)

Estimates the cross-correlation vector for complex discrete-time sequences x and y.

---

int xcorr_cmplx(complex_t* x, int nx, complex_t* y, int ny, int flag, int nr, complex_t* r, double* t)

Estimate the cross correlation \(\widehat{r}_{xy}(k)\) of vector arguments x and y or estimate autocorrelation vector if \(x = y \).

Cross-correlation vector is defined as:

\[ \widehat{r}_{xy}(k) = \frac{1}{N-k} \sum\limits_{n = 0}^{N-k-1} x(n+k)y^*(n), \qquad 0 \leq k <N; \]

\[ \widehat{r}_{xy}(k) = \frac{1}{N+k} \sum\limits_{n = 0}^{N+k-1} y^*(n-k)x(n), \qquad -N < k < 0. \]

here \( N = \max(n_x, n_y) \).

This function uses the FFT algorithm to estimate the scaled correlation vector:

\[ \breve{r}_{xy}(k) = \operatorname{IFFT}\Big[ \operatorname{FFT}\big[ \mathbf{x} \big] \operatorname{FFT}^*\big[ \mathbf{y} \big] \Big] \]

Parameters

[in]	x	Pointer to the discrete-time vector x. Vector size is [nx x 1].
[in]	nx	Size of vector x.
[in]	y	Pointer to the discrete-time vector y. Vector size is [ny x 1].
[in]	ny	Size of vector y.
[in]	flag	Flag specifies the type of scaling applied to the correlation vector \(\breve{r}_{xy}(k)\). Is one of: DSPL_XCORR_NOSCALE unscaled correlation vector from IFFT output \(\breve{r}_{xy}(k)\); DSPL_XCORR_BIASED biased correlation vector \(\breve{r}_{xy}(k)/N \); DSPL_XCORR_UNBIASED unbiased correlation vector \(\widehat{r}_{xy}(k) = \frac{\breve{r}_{xy}(k)}{N-|k|} \);
[in]	nr	Maximum correlation lag. Correlation vector \(\widehat{r}_{xy}(k)\) is calculated for \( k= -n_r,\,\, -n_r +1, \ldots n_r\).
[out]	r	Pointer to the cross-correlation or autocorrelation vector. Vector size is [(2*nr+1) x 1]. Memory must be allocated.
[out]	r	Pointer to the cross-correlation argument vector \( k= -n_r,\,\, -n_r +1, \ldors n_r\). Vector size is [(2*nr+1) x 1]. Pointer can be NULL.

Returns

RES_OK if function returns successfully.
Else code error.

Author

Sergey Bakhurin www.dsplib.org

Definition at line 449 of file xcorr.c.