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→The Method of Reassignment: fixed equation alignment |
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true region of support of the analyzed signal.
== The
One of the best-known time-frequency representations is the
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A time-frequency representation having improved resolution,
relative to the spectrogram, is the [[Wigner
which may be interpreted as a short-time
Fourier transform with a window function that is perfectly
matched to the signal. The Wigner
highly-concentrated in time and frequency, but it is also
highly nonlinear and non-local. Consequently, this
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[[Cohen's class distribution function|Cohen's class]] of
bilinear time-frequency representations is a class of
"smoothed" Wigner
kernel that can reduce sensitivity of the distribution to
noise and suppresses cross-components, at the expense of
smearing the distribution in time and frequency. This
smearing causes the distribution to be non-zero in regions
where the true Wigner
The spectrogram is a member of Cohen's class. It is a
smoothed Wigner
equal to the Wigner
window. The method of reassignment smoothes the Wigner
distribution, but then refocuses the distribution back to
the true regions of support of the signal components. The
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support of the analyzed signal.
== The
Pioneering work on the method of reassignment was first
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spectrogram is zero-valued.
== Efficient
In digital signal processing, it is most common to sample
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\end{matrix}</math></center>
where <math>W_{x}(t,\omega)</math> is the Wigner
distribution of <math>x(t)</math>, and
<math>\Phi(t,\omega)</math> is the kernel function that
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