In an ideal world, the measurement noise in gravitational wave data would be stationary and Gaussian. In reality, neither of these conditions holds. Here a general framework is introduced that can be used to model nonstationary noise in an easily interpretable way, using a dynamic power spectrum $S(f,t)$. The construction is a Gram-factor model for the noise covariance matrix that is positive semidefinite by construction. This construction generalizes the familiar stationary power spectrum $S(f)$. The dynamic spectrum encodes the properties of the noise covariance matrix in any basis, including the frequency domain, time domain, and time-frequency wavelet domain. Closed form expressions are given for discrete Fourier representations of the data, and for discrete Wilson-Daubechies wavelet representations of the data. Both take the form of Gramian matrices. Examples are provided, including the nonstationarity caused by window functions, the modulated response to galactic binary signals for space-based detectors, and other, more general types of nonstationarity.

Close

PrevNext

View figure in article

• Gravitational wave detection