You are given two sets of time$-$series data collected from older healthy adults $($subj$\_$A & subj$\_$B$).$Each set contains four curated $($i$.$e$.$ pre$-$processed$)$ time$-$series datasets representing continuous de$-$meaned contemporaneous $($i$.$e$.$ synchronized for each set$)$ samples every $0\mathrm{.}5$ s$.$

$(1)$ De$-$meaned systemic Mean Arterial Blood Pressure $($extension $.$bp$)$ measured at the index finger via photo$-$plethysmography $($in mmHg$),$ which is the average value of highly$-$sampled arterial blood pressure over each cardiac cycle $($R$-$R interval of the respective electrocardiogram$),$ properly pre$-$processed to generate evenly sampled time$-$series data.

$(2)$ De$-$meaned Mean Cerebral Blood Flow Velocity $($extension $.$fv$))$ measured at the right middle cerebral artery $($MCA$)$ via transcranial Doppler $($in cm$/$s$),$ which is the average value of highly$-$sampled cerebral blood flow velocity at the MCA over each cardiac cycle $($R$-$R interval$),$ properly pre$-$processed to generate evenly sampled time$-$series data.

$(3)$ De$-$meaned Heart Rate $($extension $.$hr$)$ defined as the inverse of the R$-$R interval of each cardiac cycle $($in beats$/$min$),$ which is extracted from the highly sampled electrocardiogram $($or equivalently from the arterial blood pressure signal$)$ and properly pre$-$processed to generate evenly sampled time$-$series data.

$(4)$ De$-$meaned end$-$tidal CO$2($extension $.$co$2)$ measured via capnography using a nasal cannula $($in mmHg$),$ which is extracted at each breath from the highly sampled capnogram $($peak value at end of exhalation$)$ and properly pre$-$processed to generate evenly sampled time$-$series data

The applied pre$-$processing of these time$-$series datasets includes $($a$)$ high$-$pass filtering above $0\mathrm{.}005$ Hz $($which includes de$-$meaning$)$ and $($b$)$ clipping of occasional outliers.

You are asked to:

$(4)$ Compute the cross$-$correlation function estimates $($using max lag of $100$ samples$)$ and the respective cross$-$spectra between $($a$)$ bp & fv$,($b$)$ bp & hr$,($c$)$ co$2$ & fv$,($d$)$ co$2$ & hr for each subject. Compare the results for the two subjects.

This is MATLAB