[SciPy-Dev] Pull Req: Add periodogram and welch functions

Till Stensitzki mail.till@gmx...
Wed Dec 5 06:03:42 CST 2012

> You don't. The variance of the periodogram is independent of its length. But
intuitively, sampling more
> data should produce a better estimate of the power spectrum: The
power-spectrum is the Fourier transform
> of the signal's autocorrelation. The more data we sample, the better we can
estimate the autocorrelation
> – and thus the better we can estimate the spectrum. But the periodogram does
not work that way. As a
> spectrum estimator, its variance does not decay with the amount of sampled
data. That is what Welch,
> Blackman-Tuckey, and multitaper methods tries to remedy, but they do so by
introducing bias. 
> Personally I prefer ARMA modelling or continous wavelet transform for spectrum
> For FFT-based power spectra, a surprisingly efficient method is to wavelet
denoise a multitaper
> spectrum. Multitapering seems to work better than Welch, and after wavelet
shrinkage the spectra look
> smooth. But still this is inferior to using parametric ARMA modelling – or
just averaging a CWT over time.
> Sturla

The book from Larry Bretthorst "Bayesian Spectrum Analysis and Parameter 
Estimation." shows nicely how spectrum estimation fits into (bayessian-)
statistics. It can be downloaded from his site:


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