Exploiting early time response using the half Fourier transform (HFT) for parameter estimation

This paper present a new technique for estimating parameters (frequencies and damping factors) of early time responses. An early time response is composed of damped sinusoids and impulse-like components. Due to the impulse-like components, it is difficult to extract meaningful damped sinusoids. The new technique uses fractional Fourier transforms (FrFT) especially the half Fourier transform (HFT). Unlike the normal Fourier transform, the HFTs of an impulse and a damped exponential are similar, so, impulse components can be separated from the damped exponentials in the HFT domain, which was not possible when using previous techniques. The result from several examples shows that the new technique is good for both damped and undamped exponentials which have impulse-like components.