Constrained, optimal tapers using the Riedel & Sidorenko–Parker method
Estimates the optimal number of tapers at each frequency of given PSD, using a modified Riedel-Sidorenko MSE recipe (RS-RLP).
riedsid(PSD, ...)
## S3 method for class 'spec'
riedsid(PSD, ...)
## Default S3 method:
riedsid(
PSD,
ntaper = 1L,
tapseq = NULL,
Deriv.method = c("local_qls", "spg"),
constrained = TRUE,
c.method = NULL,
verbose = TRUE,
...
)
riedsid2(PSD, ...)
## S3 method for class 'spec'
riedsid2(PSD, ...)
## Default S3 method:
riedsid2(
PSD,
ntaper = 1L,
constrained = TRUE,
verbose = TRUE,
fast = FALSE,
riedsid_column = 0L,
...
)PSD |
vector or class |
... |
optional arguments passed to |
ntaper |
scalar or vector; number of tapers to apply optimization |
tapseq |
vector; representing positions or frequencies (same length as |
Deriv.method |
character; choice of gradient estimation method |
constrained |
logical; apply constraints with |
c.method |
string; constraint method to use with |
verbose |
logical; should messages be printed? |
fast |
logical; use faster method? |
riedsid_column |
scalar integer; which column to use in multivariate optimization. If the value is 0 the maximum number of tapers for all columns is chosen. If the value is < 0 the minimum number of tapers for all columns is chosen. If the value is 1, 2, 3, etc. the number of tapers is based on the column selected. |
The optimization is as follows. First, weighted derivatives of the input PSD are computed. Using those derivatives the optimal number of tapers is found through the RS-RLP formulation. Constraints are then placed on the practicable number of tapers.
riedsid2 is a new (faster) implementation which does not allow
for multiple constraint methods; this is the preferred function to use.
The parameter c.method provides an option to change the method
of taper constraints. A description of each may be found in
the documentation for constrain_tapers.
Once can use constrained=FALSE to turn off all taper constraints; this
could lead to strange behavior though.
The parameter Deriv.method determines which method is used
to estimate derivatives.
"local_qls" (default) uses quadratic weighting and
local least-squares estimation; this can be slower than "spg".
"spg" uses splineGrad; then, additional arguments
may be passed to control the smoothness of the derivatives
(e.g spar in smooth.spline).
Object with class 'tapers'
The "spg" can become numerically unstable, and it's not clear when it will
be the preferred over the "local_qls" method, other than for efficiency's sake.
A.J. Barbour adapted original by R.L. Parker
## Not run: #REX
library(psd)
##
## Riedel-Sidorenko-Parker taper optimization
##
set.seed(1234)
# some params
nd <- 512 # num data
ntap <- 10 # num tapers
nrm <- 40 # sharpness of the peaks rel 2*variance
#
# create a pseudo spectrum
# with broad peaks
x <- 0:(nd-1)
riex <- rnorm(nd) + nrm*abs(cos(pi*x/180) + 1.2)
riex <- riex + 8*nrm*dcauchy(x, nd/3)
riex <- riex + 5*nrm*dnorm(x, nd/2)
# some flat regions
riex[riex<25] <- 25
ried <- dB(riex, invert=TRUE)
# optimize tapers
rtap <- riedsid(riex, ntaper=ntap) # deprecation warning
rtap2 <- riedsid2(riex, ntaper=ntap)
rtap3 <- riedsid2(riex, ntaper=ntap, fast=TRUE)
# plot
op <- par(no.readonly = TRUE)
par(mfrow=c(2,1), mar=rep(1.3,4), mai=rep(0.6,4))
# ... the mock spectrum
plot(riex, type="h", xaxs="i", ylim=c(0,200),
main='Pseudo-spectrum')
# ... tapers
plot(rtap2, col=NA, xaxs="i",
main='Original and Optimized tapers',
ylim=c(0,max(c(ntap, rtap,rtap2,rtap3))))
# original tapers:
abline(h=ntap, lty=2)
# optimized tapers
lines(rtap, col="red")
# 2 and 2-fast
lines(rtap2, lwd=3, col="blue")
lines(rtap3, col="cyan")
par(op)
## End(Not run)#REXPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.