NAG Library Function Document

nag_tsa_gain_phase_bivar (g13cfc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{xg}\left[\mathbf{ng}\right]$ – const doubleInput

On entry: the ng univariate spectral estimates, $f_{xx}\left(\omega \right)$, for the $x$ series.

2:    $\mathbf{yg}\left[\mathbf{ng}\right]$ – const doubleInput

On entry: the ng univariate spectral estimates, $f_{yy}\left(\omega \right)$, for the $y$ series.

3:    $\mathbf{xyg}\left[\mathbf{ng}\right]$ – const ComplexInput

On entry: $f_{xy}\left(\omega \right)$ the ng bivariate spectral estimates for the $x$ and $y$ series. The $x$ series leads the $y$ series.

Note: the two univariate and the bivariate spectra must each have been calculated using the same amount of smoothing. The frequency width and the shape of the window and the frequency division of the spectral estimates must be the same. The spectral estimates and statistics must also be unlogged.

4:    $\mathbf{ng}$ – IntegerInput

On entry: the number of spectral estimates in each of the arrays xg, yg and xyg. It is also the number of gain and phase estimates.

Constraint: $\mathbf{ng}\ge 1$.

5:    $\mathbf{stats}\left[4\right]$ – const doubleInput

On entry: the 4 associated statistics for the univariate spectral estimates for the $x$ and $y$ series. $\mathbf{stats}\left[0\right]$ contains the degrees of freedom, $\mathbf{stats}\left[1\right]$ and $\mathbf{stats}\left[2\right]$ contain the lower and upper bound multiplying factors respectively and $\mathbf{stats}\left[3\right]$ holds the bandwidth.

Constraint: $\mathbf{stats}\left[0\right]\ge 3.0$.

6:    $\mathbf{gn}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng gain estimates, $\hat{G}\left(\omega \right)$, at each frequency $\omega$.

7:    $\mathbf{gnlw}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng lower bounds for the ng gain estimates.

8:    $\mathbf{gnup}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng upper bounds for the ng gain estimates.

9:    $\mathbf{ph}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng phase estimates, $\hat{\varphi }\left(\omega \right)$, at each frequency $\omega$.

10:  $\mathbf{phlw}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng lower bounds for the ng phase estimates.

11:  $\mathbf{phup}\left[\mathbf{ng}\right]$ – doubleOutput

On exit: the ng upper bounds for the ng phase estimates.

12:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BIVAR_SPECTRAL_ESTIM_ZERO

A bivariate spectral estimate is zero.

For this frequency the gain and the phase and their bounds are set to zero.

NE_INT_ARG_LT

On entry, $\mathbf{ng}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ng}\ge 1$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_REAL_ARG_LT

On entry, $\mathbf{stats}\left[0\right]$ must not be less than 3.0: $\mathbf{stats}\left[0\right]=〈\mathit{\text{value}}〉$.

NE_SQUARED_FREQ_GT_ONE

A calculated value of the squared coherency exceeds one.

For this frequency the squared coherency is reset to 1.0 in the formulae for the gain and phase bounds.

NE_UNIVAR_SPECTRAL_ESTIM_NEG

A bivariate spectral estimate is negative.

For this frequency the gain and the phase and their bounds are set to zero.

NE_UNIVAR_SPECTRAL_ESTIM_ZERO

A bivariate spectral estimate is zero.

For this frequency the gain and the phase and their bounds are set to zero.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13cfce.c)

10.2

Program Data

Program Data (g13cfce.d)

10.3

Program Results

Program Results (g13cfce.r)