The dark current of a photodiode is recorded as a stationary white-noise sequence…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Scientific programming for physicists

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

Problem

The dark current of a photodiode is recorded as a stationary white-noise sequence with variance

\sigma_i^2 = 8.0\times10^{-16}\,\mathrm{A^2}

, sampled at

f_s = 4000\,\mathrm{Hz}

. ((a)) Compute the flat one-sided power spectral density

S

(in

\mathrm{A^2\,Hz^{-1}}

) that this noise must have, valid from

0

to the Nyquist frequency. ((b)) Check the Parseval normalisation by integrating

S

from

0

to the Nyquist frequency and confirming it reproduces

\sigma_i^2