Analysis and application of digital spectral warping in analog and mixed-signal testing

Spectral warping is a digital signal processing transform which shifts the frequencies contained within a signal along the frequency axis. The Fourier transform coefficients of a warped signal correspond to frequency-domain 'samples' of the original signal which are unevenly spaced along the frequency axis. This property allows the technique to be efficiently used for DSP-based analog and mixed-signal testing. The analysis and application of spectral warping for test signal generation, response analysis, filter design, frequency response evaluation, etc. are discussed in this paper along with examples of the software and hardware implementation

Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. The joint coherent analysis of GW by multiple detectors can improve the sight horizon, the estimation of the source location and the wave polarization angles. Here, we extend the BCC search to the multiple detector case. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time-series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure

Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries

Frequency-domain filters for time-windowed gravitational waves from inspiralling compact binaries are constructed which combine the excellent performance of our previously developed time-domain P-approximants with the analytic convenience of the stationary phase approximation without a serious loss in event rate. These Fourier-domain representations incorporate the ``edge oscillations'' due to the (assumed) abrupt shut-off of the time-domain signal caused by the relativistic plunge at the last stable orbit. These new analytic approximations, the SPP-approximants, are not only `effectual' for detection and `faithful' for parameter estimation, but are also computationally inexpensive to generate (and are `faster' by factors up to 10, as compared to the corresponding time-domain templates). The SPP approximants should provide data analysts the Fourier-domain templates for massive black hole binaries of total mass m less than about 40 solar mases, the most likely sources for LIGO and VIRGO.Comment: 50 Pages, 10 Postscript figures, 7 Tables, Revtex, Typos corrected, References updated, Additions on pages 25, 26 and 3

SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm

Using EMD-FrFT filtering to mitigate high power interference in chirp tracking radars

This letter presents a new signal processing subsystem for conventional monopulse tracking radars that offers an improved solution to the problem of dealing with manmade high power interference (jamming). It is based on the hybrid use of empirical mode decomposition (EMD) and fractional Fourier transform (FrFT). EMD-FrFT filtering is carried out for complex noisy radar chirp signals to decrease the signal's noisy components. An improvement in the signal-to-noise ratio (SNR) of up to 18 dB for different target SNRs is achieved using the proposed EMD-FrFT algorithm