An ultrasound transducer for medical imaging emits a pulse whose envelope is well…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier transforms, spectra and convolution

Problem

An ultrasound transducer for medical imaging emits a pulse whose envelope is well modelled as a Gaussian,

|f(t)|\propto e^{-t^2/2\tau^2}

, with a half-width at half maximum of

\Delta t = 0.50\,\mu\text{s}

. Estimate the half-width at half maximum

\Delta f

of the frequency spectrum of this pulse.

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