A signal generator produces a pure tone at exactly

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Computational Physics, Ch Spectra of sampled signals

Problem

A signal generator produces a pure tone at exactly f0=60.25 Hzf_0 = 60.25\,\mathrm{Hz}. It is sampled at fs=1000 Hzf_s = 1000\,\mathrm{Hz} for N=2000N = 2000 samples. (a) Find the bin spacing Δf\Delta f of this record. (b) Find how many cycles of the tone the record holds, and hence say where the true frequency falls relative to the two nearest bin centres. (c) Keeping fs=1000 Hzf_s = 1000\,\mathrm{Hz} fixed, find the shortest record length TrecT_{\rm rec} (in seconds) for which f0f_0 falls exactly on a bin centre, and state the corresponding NN.

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