A record consists of samples of with

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Scientific Computing for Physicists, Ch Spectra with error bars: the fast transform, convolution and spectral estimation

Problem

A record consists of samples of

x_n = A\cos(2\pi f_0 t_n)

with

A = 3.0\,\mathrm{V}

, where

f_0

is chosen to fall exactly on a discrete Fourier bin of a record of

N = 4096

samples (no leakage). State the total power that must be recovered by integrating the one-sided PSD across the peak at

f_0

, and give its numerical value.