PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Electronics, Instrumentation & Communication · Scientific programming for physicists
Scientific Computing for Physicists, Ch Spectra with error bars: the fast transform, convolution and spectral estimation
Problem
A seismometer record of N=32768 samples, taken at fs=100Hz, is analysed by Welch's method: it is cut into K=32 non-overlapping segments of M=1024 samples each, and the periodograms of the segments are averaged.
((a)) State the relative uncertainty of the resulting spectral estimate at each frequency, assuming the segments are statistically independent.
((b)) State the frequency resolution of the Welch estimate.