A microphone next to a machine records two engine tones at and

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Computational Physics, Ch Spectra of sampled signals

Problem

A microphone next to a machine records two engine tones at

220.0\,\mathrm{Hz}

and

220.5\,\mathrm{Hz}

, sampled at

f_s = 4000\,\mathrm{Hz}

. A Hann-windowed spectrum needs about

2.46

times the record length that an unwindowed one needs to resolve the same pair of lines (the same factor found for the pendulum's close modes). (a) Find the shortest unwindowed record length

T_{\rm rec}

that resolves the two tones, and the corresponding number of samples

N

. (b) Find the shortest Hann-windowed record length and its corresponding

N

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