LAL  7.5.0.1-89842e6
Module ComputeTransfer.c

## Detailed Description

Computes the transfer function from zero-pole-gain representation.

A transfer function can either be specified as a list of coefficients or a list of poles and zeros. The function LALComputeTransfer() computes the frequency representation of the transfer function calrec->transfer described by the zeroes, poles and gain in *calrec. The memory for the frequency series should be allocated before calling this routine which uses calrec->transfer->deltaF and calrec->transfer->data->npoints.

The routine LALUpdateCalibration() updates the response function and the sensing function from some reference functions to the current functions using information about the calibration lines. The two calibration lines yield two constants (as a slowly-varying function of time) that are used as coefficients to the reference response and sensing functions to compute the current response and sensing functions. These coefficients are stored in time series in the parameter structure, along with the current epoch and duration for which the calibration functions are to be computed. If the duration is zero, the calibration factors are the first ones at or after the given epoch. If the duration is non-zero, then the calibration factors are an average of all calibrations between epoch and epoch + duration.

The routine LALResponseConvert() takes a given frequency series and converts it to a new frequency series by performing the following steps: (i) the original frequency series is interpolated (using linear interpolation of the real and imaginary parts independently) to the frequencies required in the output frequency series; (ii) if the output frequency series has units that are the inverse of those of the input frequency series, the data is inverted; (iii) the data is scaled by an appropriate power of ten computed from the input units and the output units. For example you can convert from strain per count to counts per atto-strain.

### Algorithm

The transfer function is deduced from the poles and zeros as follows:

$$T(f) = c_{\mathrm{gain}} {\prod_i \textrm{zero}(f,z_i)}{ \prod_{i} \textrm{pole}(f,p_i)}$$

where

$$\textrm{zero}(f,z) = \left\{ \begin{array}{ll} (i f / z) + 1 & \textrm{ when } z\neq 0 \\ i f & \textrm{ when } z = 0 \end{array} \right.$$

and

$$\textrm{pole}(f,p) = \left\{ \begin{array}{ll} \frac{1}{(i f / p) + 1} & \textrm{ when } p \neq 0 \\ \frac{1}{i f} & \textrm{ when } p = 0 \end{array} \right.$$

For both the transfer function and the pole-zero notation the units for frequency is Hz rather than rad/s (angular frequency). In particular, poles and zeros are specified by their location in frequency space

To update the response function from one epoch to another, two functions are needed. These are the sensing function $$C(f)$$ and the response function $$R(f)$$, which are related by

$$R(f) = \frac{1+H(f)}{C(f)}$$

where $$H(f)$$ is the open-loop gain function. If the sensing function and the open-loop gain function are known at some reference time ( $$C_0(f)$$ and $$H_0(f)$$) then the sensing function and open-loop gain function can be calculated at a later time. They are $$C(f)=\alpha C_0(f)$$ and $$H(f)=\alpha\beta H_0(f)$$ where $$\alpha$$ and $$\beta$$ are slowly varying coefficients that account for overall changes in the gains of the sensing function and the open-loop gain. The coefficients $$\alpha$$ and $$\alpha\beta$$ can be determined, as slowly-varying functions of time, by monitoring the two injected calibration lines. Thus, an updated sensing function and response function can be computed from reference sensing function and response function, $$C_0(f)$$ and $$R_0(f)$$ via:

$$C(f) = \alpha C_0(f)$$

and

$$R(f) = \frac{1+\alpha\beta[C_0(f)R_0(f)-1]}{\alpha C_0(f)}$$

where $$\alpha$$ and $$\beta$$ are those values of the coefficients that are appropriate for the particular epoch.

### Notes

The DC component of calrec->transfer is always filled with $$1 + i 0$$. In most cases, this should be irrelevant for gravitational wave data analysis, but care should be taken if DC is relevant when this function is used.

## Prototypes

void LALComputeTransfer (LALStatus *stat, CalibrationRecord *calrec)
UNDOCUMENTED. More...

void LALUpdateCalibration (LALStatus *status, CalibrationFunctions *output, CalibrationFunctions *input, CalibrationUpdateParams *params)
UNDOCUMENTED. More...

void LALResponseConvert (LALStatus *status, COMPLEX8FrequencySeries *output, COMPLEX8FrequencySeries *input)
UNDOCUMENTED. More...

INT4 XLALResponseConvert (COMPLEX8FrequencySeries *output, COMPLEX8FrequencySeries *input)
UNDOCUMENTED. More...

## ◆ LALComputeTransfer()

 void LALComputeTransfer ( LALStatus * stat, CalibrationRecord * calrec )

UNDOCUMENTED.

Definition at line 137 of file ComputeTransfer.c.

## ◆ LALUpdateCalibration()

 void LALUpdateCalibration ( LALStatus * status, CalibrationFunctions * output, CalibrationFunctions * input, CalibrationUpdateParams * params )

UNDOCUMENTED.

Definition at line 210 of file ComputeTransfer.c.

## ◆ LALResponseConvert()

 void LALResponseConvert ( LALStatus * status, COMPLEX8FrequencySeries * output, COMPLEX8FrequencySeries * input )

UNDOCUMENTED.

Definition at line 422 of file ComputeTransfer.c.

## ◆ XLALResponseConvert()

 INT4 XLALResponseConvert ( COMPLEX8FrequencySeries * output, COMPLEX8FrequencySeries * input )

UNDOCUMENTED.

Definition at line 538 of file ComputeTransfer.c.