Function: sp_filters()

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void sp_filters(float m1, float m2, float *ch1, float *ch2, float fstart, int n, float srate, float f_c, float t_c, int order)
This function generates stationary phase approximations to binary inspiral chirp waveforms. Its input and output are similar to make_filters(). The difference is that the chirps are generated in the frequency domain using the stationary phase approximation.

The arguments are:

m1: Input. The mass of body-1 in solar masses.

m2: Input. The mass of body-2 in solar masses.

ch1: Output. Upon return, ch1[0..n-1] contains the stationary phase approximation to $\tilde{h}_c(f)$ [Eq. ()] in the same format as would be returned by a realft() of a time-domain function sampled at rate srate. That is, except for DC and Nyquist frequencies, ch1[2*i] and ch1[2*i+1] contain respectively the real and imaginary parts of $\tilde{h}_c(f)$ for $f={\tt i*srate/n}$. This function sets ch1[0] (DC) and ch1[1] (Nyquist) to zero. The chirp is also set to zero for $f<{\tt fstart}$ and for $f>{\tt f\_c}$ (see section  for $f_c$). The output ch1[0..n-1] has dimensions of 1/Hz.

ch2: Output. Upon return, ch2[] contains $\tilde{h}_s(f)$ in the same way that ch1[] contains $\tilde{h}_c(f)$.

fstart: Input. The starting gravitational-wave frequency of the chirp in Hz. Note: this is twice the orbital frequency!

n: Input. The length of the arrays ch1[0..n-1] and ch2[0..n-1].

srate: Input. The sample rate, in Hz.

f_c: Input. The coalescence frequency $f_c$, as described in section . This is the high-frequency cutoff of the chirps.

t_c: Input. The coalescence time, in seconds. Note this is the time of the end of the chirp (see section ).

order: Input. Order of generated chirps in $(\pi MfT_\odot/M_\odot)^{1/3}$ (twice the post-Newtonian order).

This function assumes that you have already allocated storage for the chirps.

Author: Benjamin Owen, owen@tapir.caltech.edu

Comments: The sp_filters() function doesn't include spins yet. It will be simple to add higher-order post-Newtonian phase terms as they appear in the literature.