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Linearly Swept Frequency Measurements, Time-Delay Spectrometry, and the Wigner Distribution
The theory of linearly swept frequency measurements and time-delay spectrometry is reexamined and the Wigner distribution is introduced. It is shown that such measurements can be described in terms of a linear transformation of the coordinates of the Wigner distribution of the system impulse response, and that the measurement as normally carried out is incomplete. A further operation on the signal yields a more exact estimation of the transfer function, which has no dependence on the sweep rate used for the measurement. Hence the sweep rate limitation may be ignored. It is further shown that time-delay spectrometry produces a windowed version of the system impulse response and that as a result the energy-time-frequency curve is equivalent to the spectrogram of the impulse response. The energy-time curve is also examined and is related to the Wigner distribution of the analytic impulse response.
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