Parametric PSD window to data

Question

I have question abouth parametric spectrum density (PSD) estimation using Yule-Walker (autocorrelation method) equation, which relays on autocorelation:

And it's mention: "However, since the autocorrelation method applies a rectangular window to the data, the data will be extrapolated with zeros. As a consequence, the resolution of estimates is lower…"

Another parametric PSD estimation is covariance which relays equation:

And it's mention: "The advantage of the covariance method over the autocorrelation method is that no windowing of the data is required in the formation of the autocorrelation estimates rx(k,l)."

So I don't understand from where this window for data.

Answer 1

If you imagine the window or partial response pulse response curve as a sliding time shutter to incoming data, and the weighting for each bit is determined by this algorithm, which in the "acf" rectangular window is the matrix which scales data bit according to a fraction of the previous and post bit signal-amplitudes. This becomes a partial response curve that looks like a single pulse going thrue bandpass filter.

The shape of the function is to provide a " Matched Filter" to the signal bandwidth and thus that optimizes the S/N ratio. ( communication Theory)

"Acf and pacf" use the fact that the timeseries is stationary, so that autocovariance elements are a function of the lag only, not the exact time limits.

This algorithm is also used for digital sync patterns, when looking for word or frame sync, if they choose a pattern that has a sharp weighed match when in SYNC and the pattern shows more bits that do not match this unique sync pattern the further you move away from SYnc in increments of 1bit . This is how they design sync patterns for frame sync in SDLC, modems, and high speed synchronous communication .

So the sliding window of data is a shift register used to search for a pattern match based on "acf" theory.