Power Spectrum Probability Vector Calculator

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Description

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

Usage

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

Arguments

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

Details

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.

Value

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

Author(s)

Vitaly Efremov <vitaly.efremov@dcu.ie>

References

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.

See Also

crit.stheorem, cxds.stheorem, d2spec

Examples

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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)