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The identification of a linear time-invariant (LTI) system h(
n) with only noisy output measurements is very important in
many signal processing areas such as seismic deconvolution,
channel equalization in communications, radar, sonar,
speech processing and image processing. Recently, cumulant
based identification of nonminimum-phase LTI systems with
only non-Gaussian output measurements has drawn extensive
attention in the previous signal processing areas because
cumulants, which are blind to any kind of a Gaussian
process, can be used to not only extract the amplitude
information but also the phase information of $h(n)$, meanwhile
they are inherently immune from Gaussian measurement noise.
This paper presents a new cumulant based phase estimation
method with only non-Gaussian measurements x(n) contaminated by
Gaussian noise for an unknown (minimum or nonminimum-phase)
linear time-invariant (LTI) system h(n). The proposed method
estimates the phase of h(n) by processing x(n) with an allpass
filter such that the output y(n) has a maximum Mth-order (M
greater or equal to 3$) cumulant in absolute value. Amplitude
response estimation of h(n) is not involved throughout the
proposed method as methods which estimate the phase of h(n)
only from the phase of polyspectra of x(n). Moreover, it does
not need any preprocessing of x(n) with a correlation based
whitening filter, which is noise sensitive and crucially limits
the estimation accuracy of system phase, as needed by the well-
known minimum-phase (MP) - allpass (AP) decomposition based
methods. Some simulation results followed by some experimental
results with real speech data are provided to support the
proposed cumulant based phase estimation method. Finally, the
paper concludes with some conclusions.
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