Function: find_chirp()

0 void find_chirp(float* htilde, float* ch0tilde, float* ch90tilde, float* twice_inv_noise, float n0, float n90, float* output0, float* output90, int n, int chirplen, int* offset, float* snr_max, float* c0, float* c90, float *var)
This routine filters the gravity-wave strain through a pair of optimal filters corresponding to the two phases of a binary chirp, then finds the time at which the SNR peaks.

The arguments are:

htilde: Input. The FFT of the gravity-wave strain.

ch0tilde: Input. The FFT of the 0-degree chirp.

ch90tilde: Input. The FFT of the 90-degree chirp (assumed orthogonal to the 0-degree chirp).

twice_inv_noise: Input. Twice the inverse noise power spectrum, used for optimal filtering. The array element twice_inv_noise[0] contains the DC value, and the array element twice_inv_noise[n/2] contains the value at the Nyquist frequency.

n0: Input. Normalization of the 0-degree chirp.

n90: Input. Normalization of the 90-degree chirp.

output0: Output. A storage array. Upon return, contains the filter output of the 0-degree phase optimal filter.

output90: Output. A storage array. Upon return, contains the filter output of the 90-degree phase optimal filter.

n: Input. Defines the lengths of the various arrays: ch0tilde[0..n-1], ch90tilde[0..n-1], output0[0..n-1], output90[0..n-1], and twice_inv_noise[0..n/2].

chirplen: Input. The number of bins in the time domain occupied by the chirp that you are searching for. This is necessary in order to untangle the wrap-around ambiguity explained earlier.

offset: Output. The offset, from 0 to n-chirplen-1, at which the signal output (for an arbitrary linear combination of the two filters) peaks.

snr_max: Output. The maximum signal-to-noise ratio (SNR) found.

c0: Output. The coefficient of the 0-phase template which achieved the highest SNR.

c90: Output. The coefficient of the $90^\circ$-phase template which achieved the highest SNR. Note that $c_0^2 + c_{90}^2$ should be 1.

var: Output. The variance of the filter output. Would be 1 if the input to the filter were colored Gaussian noise with a spectrum defined by $S_h$.

Author: Bruce Allen, ballen@dirac.phys.uwm.edu

Comments: None.