lowpass filtered expected correlation of powerlaw signal pair

Correlation of two timeseries with powerlaw signal and powerlaw noise evaluated until f this equals the correlation of linearly coupled lowpass filtered powerlaw process

Usage

PSP.CorUntilF(f, betaSignal, betaNoise, N, r)

Arguments

f

frequency until which to integrate

betaSignal

powerlaw slope of the signal

betaNoise

powerlaw slope of the noise

N

Number of points per timeseries

r

expected correlation of the unfiltered

Value

expected correlation of the timeseries

Author

Thomas Laepple

Examples

temp <- replicate(1000,PSP.CorAfterRollmean(1000,1,0,0.5))
rowMeans(temp)
#> [1] 0.4998948 0.8218859 0.9308612
PSP.CorUntilF(f=c(0.5,0.5/10,0.5/50),betaSignal=1,betaNoise=0,N=1000,r=0.5)
#> [1] 0.5000000 0.8253528 0.9341159