### 2.4 General form of the response function

In many cases of interest the response function of the detector to a plane gravitational wave
can be written as a linear combination of waveforms [which all depend on the
same set of parameters ] with constant amplitudes (),
where the vector collects all the signal’s parameters. It is convenient to introduce column matrices
Then one can briefly write and the response (30) can be written as
The functions () are independent of the parameters . The parameters are called
extrinsic (or amplitude) parameters whereas the parameters are called intrinsic.
Eq. (32) with is a model of the response of the space-based detector LISA to gravitational
waves from a binary system [78]. Also for the same equation models the response of a
ground-based detector to a continuous source of gravitational waves like a rotating neutron star [68]. For
ground-based detectors the long-wavelength approximation can be applied and within this approximation
the functions () are given by

where is the phase modulation of the signal and and are slowly varying
amplitude modulations. The gravitational-wave signal from spinning neutron stars may consist of several
components of the form (32). For short observation times over which the amplitude modulation functions
are nearly constant, the response of the ground-based detector can further be approximated by
where and are constant amplitude and initial phase, respectively, and is a slowly varying
function of time. Eq. (34) is a good model for the response of a detector to the gravitational wave from a
coalescing compact binary system [135, 30]. We would like to stress that not all deterministic
gravitational-wave signals may be cast into the general form (32).