The band-pass filter is performed on (10) in the range direction for each slow-time index n; the outputs are: Lambda left[m,nright]={chi}_1Wleft[m,nright]+{chi}_2Wleft[m-1,nright]+{chi}+{chi}_{N_b+1}Wleft[m-{N}_b,nright]-{kappa}_2Wleft[m-1,nright]-dots -{kappa}_{N_a+1}Wleft[m-{N}_a,nright] (12 where N b = N a = 5 and κ i and χ i are the filter coefficients.
Instead he would increase spending for government Pell Grants to needy students, and for the first time index the maximum yearly grant for inflation.
For each time point, an index was calculated using a probit factor model and estimated factor loadings for each item were used to represent a "wealth" measure (see Ginsburg et al., 2011 for further details of this measure).
Time is divided into discrete time slots that have variable durations [t i,ti+1], represented by a set of slot index I=1,2,…,m, where 0≤t i for time index i∈I.
For simplicity, the time index i is ignored in the following analysis.
A matrix formulation of this system for an arbitrary time index, n, is as follows.
where h is the time-step, and for simplicity the time index is given in superscript.
A total transmitted power constraint is considered, and for ease of notation, time index is dropped whenever possible.
Internal standards for quantitative and retention time index calibration were added as described in [59].
We use boldface notation to denote random processes, normal face for deterministic parameters, upper case letters for matrices, lower case letters for vectors and scalars, and subscripts for time indices.
