Power Spectrum Analysis

Question

In order to find a peak or max response in the fourier domain as in the spatial domain, I have been studying bartlett's method, welch's method, and the blackman-tukey method for more accurate power spectrum analysis after correlating two functions together in the fourier domain as depicted in this document.

But I had a few questions after reading, which I could not find in any book nor online

1) For the Bartlett method (page 11 of the pdf) what determines the value of k, or is it arbitraty. And following that, does the accuracy of the power spectrum analysis go up if k is higher, and vice versa

2) Same question as 1) but for the welch method (page 12 of the pdf)

3) For the blackman-tukey method (page 14 of the pdf), will i get the same result if I window the signal in the spatial domain, but then do the autocorrelation in the fourier domain?

Answer 1

Hopefully you understand why and in what situations those methods are used.

The integer 'K' in the Bartlett and Welch methods is not arbitrary. The value of 'K' is a "trade off" that you must make. In both methods, the greater is 'K" the lower is the variance in your final DFT results. That's a good thing. What the PSD's author doesn't tell you, though, is that the greater is 'K" the larger is your final DFT result's frequency-domain sample-to-sample spacing (measured in Hz). And that's usually a bad thing. So you must decide what value of 'K' is acceptable to you. I'm not qualified to comment on the Blackman-Tukey method.