d1spec: Power Spectrum Probability Vector Calculator
In stheoreme: Klimontovich's S-Theorem Algorithm Implementation and Data Preparation Tools

Description Usage Arguments Details Value Author(s) References See Also Examples

Function d1spec is applied to a pair of vectors (sample outcomes, observation data values, time series data, 1d signal values, etc.) and generates the pair of corresponding spectral power density functions

1	d1spec(sample0, sample1, band=c(0,0), brks=0, meansub=TRUE)

`sample0`	vector of values (sample outcomes)
`sample1`	vector of values (sample outcomes)
`band`	two border values to set a range of considered frequencies. The default c(0,0) sets full entire range i.e. from 0 to 0.5 Hz, where 1 Hz = [1/sampling_interval]
`brks`	value used in a same manner as the number of cells for the histogram. The default brks=0 sets the number of cells equal to `min(length(sample0), length(sample1))/2`
`meansub`	logical item defining if individual baseline (defined as individual mean value) is subtracted from original vectors before application of Fourier transform

Spectral power density functions are often being used as probability vectors characterizing thermodynamic states of a system. Here fast Fourier transform algorithm is utilized and the frequency values are used as 1 Hz = [1/sampling_interval], i.e. in a range from 0 to 0.5 Hz. In general the function works similarly to d1nat. As a bonus it prints basic statistics summary for power density functions alongside with technical plot. It is recommended for use as a data preparation step before following Klimontovich's S-theorem based analysis.

`f0`	spectral power density function as a probability vector representing state0 of a system
`f1`	spectral power density function as a probability vector representing state1 of a system
`freqs`	vector of coresponding frequency values

Vitaly Efremov <vitaly.efremov@dcu.ie>

T.G.Anishchenko, P.I.Saparin, N.B.Igosheva, V.S.Anishchenko. Sex differences in human cardiovascular responses to external excitation. Il Nuovo Cimento D. Luglio-Agosto 1995, Volume17, Issue7-8, pp.699-707.

E.J.Groth. Probability distributions related to power spectra. Astrophysical Journal, 1975. Suppl. Ser., Vol.29, No.286, p. 285-302.

T.Anishchenko, N.Igosheva, T.Yakusheva, O.Glushkovskaya-Semyachkina, O.Khokhlova. Normalized entropy applied to the analysis of interindividual and gender-related differences in the cardiovascular effects of stress. Eur J Appl Physiol. 2001 Aug; 85(3-4):287-98.

crit.stheorem, cxds.stheorem, d2spec

s0 <- 2+sin(c(1:128))
s1<- array(c(rep(0,8),rep(1,8)), c(256))

b<-d1spec(sample0=s0,sample1=s1); b
b<-d1spec(s0, s1, band=c(0,0.25), brks=16, meansub=FALSE); b

#example of 3-step data analysis with Klimontovich's S-theorem
# step a. Clean samples from outliers (points out of 1.4 sigmas)
a<-utild1clean(s0, s1, method='both', nsigma=1.4)
# step b. Create probability vectors. It seems that s0 has lower level
# of orderliness (Shannon entropy is higher).
b<-d1spec(a$clean0,a$clean1); b
# step c. Compare samples with Klimontovich's S-theorem. Renormalized entropy indicates 
# the opposite: s0 is more ordered and difference in Shannon entropy values was 
# due to just "thermodynamic noise" (discretization noise in this case)
crit.stheorem(b$f0,b$f1)
cxds.stheorem(b$f0,b$f1)