This Topic considers two time-domain Fourier transform properties,
namely how the spectrum is effected is a signal is scaled-in-time or
shifted-in-time. The scale-in-time theorem is important as it shows that
a signal with broad temporal coverage has a narrow spectral coverage,
and vice-versa (which itself leads to the uncertainty principle). This
property is useful for finding transform of signals of variable length
given an atomic signal as a building block. The Topic then discusses the
shift-in-time theorem, which has application in estimation of
time-delays, which in turn can lead to applications in (for example)
direction-of-arrival estimation. The importance of linear-phase as a
result of time-delay is introduced.
ELEE08021 Sensor Networks and Data Analysis 2 Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2021.
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