ESS210B
Prof. Jin-Yi Yu
Examples
qExample 1 – smooth over frequency
bands
A time
series has 900 days of record. If we do a Fourier analysis then the bandwidth will be 1/900 day-1, and each of the 450 spectral estimates will have 2 degrees of
freedom. If we averaged each 10 adjacent estimates together, then the bandwidth will be 1/90 day-1 and each estimate
will have 20 d.o.f.
qExample 2 – smooth over spectra of several time series
Suppose we have 10 time series of 900 days. If we compute spectra for each of these and then average the
individual spectral estimates for each frequency over the sample of 10 spectra, then we can derive a spectrum with a bandwidth of 1/900
days-1 where each
spectral estimate has 20 degrees of
freedom.