A vibration record has samples at

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Computational Physics, Ch Spectra of sampled signals

Problem

A vibration record has N=16N=16 samples at fs=16 Hzf_s = 16\,\mathrm{Hz}. The power Pk=∣y~k∣2P_k = |\tilde y_k|^2 has been computed for the bins up to the Nyquist bin: P0=0P_0=0, P1=0.5P_1=0.5, P2=50.0P_2=50.0, P3=1.2P_3=1.2, P4=0.1P_4=0.1, P5=0.05P_5=0.05, P6=0.02P_6=0.02, P7=0.01P_7=0.01, P8=0.005P_8=0.005 (all in the same power units), with P16−k=PkP_{16-k}=P_k for k=1,…,7k=1,\dots,7 because the record is real. (a) State the physical frequency represented by bin k=2k=2. (b) Find the fraction of the total power (summed over all 1616 bins, using the mirror relation to include the negative-frequency bins) that sits at ±f2\pm f_2.

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