Waveform Feature Extraction Based on Tauberian Approximation

A technique is presented for feature extraction of a waveform y based on its Tauberian approximation, that is, on the approximation of y by a linear combination of appropriately delayed versions of a single basis function x, i.e., y(t) = Σ
^M

_{i = 1}
a
_I
x(t - τ
_I
), where the coefficients a
_I
and the delays τ
_I
are adjustable parameters. Considerations in the choice or design of the basis function x are given. The parameters a
_I
and τ
_I
, i=1, . . . , M, are retrieved by application of a suitably adapted version of Prony's method to the Fourier transform of the above approximation of y. A subset of the parameters a
_I
and τ
_I
, i = 1, . . . , M, is used to construct the feature vector, the value of which can be used in a classification algorithm. Application of this technique to the classification of wide bandwidth radar return signatures is presented. Computer simulations proved successful and are also discussed.