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Technology Type:  Computation and Time-Series Data Analysis

Fast Chirp Transform

** Institution:  California Institute of Technology
** Inventor/Contact:  Professor Thomas A. Prince  
      Caltech Office of Technology Licensing 626.395.3822

** Patent Number:  6,509,866
** Supporting Agency:  National Science Foundation
** Technology Source:  LIGO Scientific Collaboration (LSC) members
      outside of LIGO Laboratory

 Patent Thumbnail

[dt albs]When two neutron stars combine into a single neutron star this process is described by three phases - the inspiral, merger and ringdown. In the initial inspiral stage of a binary neutron star coalescence the two stars spiral toward each other at a greater and greater angular velocity. During this inspiral phase the generated gravitational waves are expected to result in changes of gravitational strain with increasing amplitude and frequency resulting in a "up-chirp" signal. During the merger phase the prediction is much more difficult and currently rather uncertain but the signal properties are expected to be much more complex than a simple chirp. The final phase is called the ringdown phase in which the merged star undergoes damped body oscillations and is expected to create a gravitational wave characterized by a damped chirp signal where both the amplitude and frequency of the signal decrease in time which is called a "down-chirp". In general chirped signals are characterized by signals whose frequency change in time in a monotonic fashion. Chirped signals are not only seen in exotic systems like binary neutron star coalescences but are common in nature and engineering including: modern radar systems, sonar systems, femtosecond laser pulses and many natural physical phenomena, for instance those with dissipation.

As part of the LSC data analysis effort an algorithm was invented called the Fast Chirp Transform (FTC) to improve the detection and production of quasi-periodic signals. The FTC is a generalization of a multidimensional Fast Fourier Transform (FFT). Phase coefficients for boundary intervals are calculated using phase functions describing the time dependant frequency characteristic of an input signal in the time domain. A multidimensional FFT is performed on the dot product of the phase coefficients and the input signal in the frequency domain. The FCT eliminates the need for generating individual matched filters for each possible chirp waveform and allows a single algorithm to perform an optimal search over a very broad class of waveforms.

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