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