Reassignment method: Difference between revisions

Revision as of 17:26, 9 August 2012

Revision as of 17:49, 9 August 2012

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==Separability==

The short-time Fourier transform can often be used to

estimate the amplitudes and phases of the individual

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&= \frac{\partial }{\partial t} \arg\{ X(t,\omega_{0}) \}

\end{matrix}</math></center>

Thus, the partial derivative with respect to time of the

phase of the short-time Fourier transform can be used to

compute the instantaneous frequencies of the individual

components in a multi-component signal, provided only that

the components are separable in frequency by the chosen

analysis window.

[[Image:Long-window reassigned spectrogram of speech.png|thumb|400px|

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samples in <math>h(t)</math>.

In general, there areis an infinite number of equally- valid

Separability in time and in frequency is required of

components to be resolved in a reassigned time-frequency

representation. If the components in a decomposition are

separable in a certain time-frequency

representation, then the components can be resolved by that

time-frequency representation, and using the method of

reassignment, can be characterized with much greater

precision than is possible using classical methods.

In general, there are an infinite number of equally-valid

decompositions for a multi-component signal.

The separability property must be considered in the context of the

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spectrum is wider than the spacing between the harmonics

(that is, the harmonics are not separable, in frequency,

by the chosen analysis window).

== References ==