The reconstruction of periodic acoustical signals with time domain periodic
averaging requires a reliable estimate of the fundamental frequency (f
l) of the signal. The reconstruction task is particularly difficult
when the signal is “hidden” in additive noise and the signal-to-noise ratio
is poor. This is usually the case in most passive SONAR problems when
early detection and characterization of targets is required. Statistically
reliable estimates of the fundamental frequency of a noisy periodic signal
can be computed in the frequency domain using Bartlett’s smoothing procedure.
In this procedure, a long, noisy signal is segmented into M mutually
exclusive time segments and a power spectral estimate for each segment is
computed. Spectral estimates are ensemble-averaged to enhance the signal
power and reduce the residual spectral variance of the additive noise. In
Bartlett’s smoothing procedure the spectral line detection efficiency improves
with M 1/2 when M > 50.
The Bartlett’s smoothing procedure merely provides a range of values for
the fundamental frequency within a range of four times the standard deviation
of the embedded periodic signal. In the reconstruction procedure, the
noisy signal is reused to obtain one or more cycles of the “clean” signal.
In the reconstruction procedure, the noisy signal is segmented into J
mutually exclusive time segments, each exactly T seconds in length.
Ensemble averaging in the time domain of these segments recovers the required
“clean” signal with an enhancement efficiency of J 1/2 when
N >50 and when the proper value of T is used. Because
in most problems the correct value of T is not known, the enhancement
procedure is iterated over the a range of four times the standard deviation
and that iteration which provides the maximum signal-to-noise ratio is declared
the winner. For proper enhancement, an integer number of sample points must
occur in T, for each choice of T. This requires a new
sampling rate be used on the original time sequence for each choice of T.
The resampling is efficiently achieved using an FFT interpolation technique.
The algorithms are optimized for the SHARC ADSP-21060 DSP hardware and can
be used in real time applications.
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