Applications of the Hilbert Transform – A Nonparametric Method for Interpolation/Extrapolation of Data

This chapter presents a nonparametric method for the application of the principle of analytic continuation to interpolate/extrapolate system responses resulting in reduced computations. The Hilbert transform can also be used to speed up the spectral analysis of nonuniformly spaced data samples. One of the properties of the periodogram approach is that the there is a Hilbert transform relationship between the coefficients of the parameters used to evaluate the spectrum. The causality of the time domain signal, denoted as h(t), assures one that the real and imaginary components of the frequency domain response are related through the Hilbert transform. The application of the Hilbert transform for computing the spectrum of a waveform in a fast and efficient way from nonuniformly spaced data is illustrated. The Hilbert transform illustrates that the real and imaginary parts of any nonminimum phase transfer function from a causal system satisfy the relationship.