The discrete polynomial-phase transform

Bootstrap modeling of a class of nonstationary signals

“…It is seen that (12) is identically zero when β is a correct model, i.e., a model for which the components of indexed by the integers not in β are all zero so that For model β, a simple estimator of can be constructed as (13) The expected value of taken with respect to can be shown to be…”

“…The concept introduced in [9] has been later generalized by Peleg et al, who introduced the polynomial phase transform [11]- [13]. The polynomial phase signal model can be assumed linear in the parameters for a sufficiently high signal-to-noise ratio (SNR) [14].…”

“…To date, the only method specifically designed for model selection of polynomial phase sig-nals has been reported in [11] and [13]. The suggested criterion is based on the Cramér-Rao lower bound of the parameter estimators obtained with the polynomial phase transform, thus requiring knowledge of their distribution as well as the signal-to-noise power ratio (SNR).…”

Novel Parameter Estimation Method for Chirp Signals Using Bowtie Chirplet and Discrete Fractional Fourier Transform

“…Moreover, with those methods the signal has to be investigated over the full range of [0, 2 π ]. Methods based on wavelet [8,9] and Discrete Polynomial Phase Transform (DPT) are also reported [10]. Some recent works involve Discrete chirp Fourier transform for chirp rate estimation [11], and slope calculation of ambiguity function for parameter estimation [1] etc.…”

A AM/FM single component signal reconstruction using a nonsequential time segmentation and polynomial modeling

“…Additionally, we reference the local time k and initial phase θ i,0 to the segment centre in order to minimize estimation errors [8][9][10][11]. Then the phase is locally approximated by:…”