test.signal: A random function with a smooth background

In BBEST: Bayesian Estimation of Incoherent Neutron Scattering Backgrounds

Description

test.signal creates a random function that consists of peaks, a smooth background, and a Gaussian noise.

Usage

test.signal(x, lambda, sigma, x.delta, knots.n, peaks.widthRange, peaks.n)

Arguments

x	numeric vector, the x-points where data should be generated.
lambda	numeric, the mean signal magnitude.
sigma	numeric, the noise level.
x.delta	numeric, the minimum spacing allowed between spline knots. Defines background smoothness.
knots.n	numeric, a number of spline knots to generate.
peaks.widthRange	numeric vector, specifies range in peak widths.
peaks.n	numeric, the number of peaks to generate.

Details

The background is calculated as a sum of fundamental splines on the randomly generated knots. The function is a sum of the background, random peaks, and Gaussian noise.

Value

An object of type data (see set.data) with the following elements added:

knots	list with elements x and y that specify the knot positions and knot values, respectively.
bkg	numeric vector containing the generated background.

Examples

# 1. Create test function 
f <- test.signal(x=seq(0,30,0.01), lambda=5, 
         sigma=0.1, x.delta=1.0, knots.n=5, 
         peaks.widthRange=c(0.1, 0.3), peaks.n=7)
	
# 2. Plot results
plot(f$x, f$y, t="l", xlab="x", ylab="f")
lines(f$x, f$bkg, col=2)
lines(f$x, f$y - f$bkg, col="gray")
legend(20, .9*max(f$y), c("test function", "background", 
       "peaks+noise"), lty=1, col=c(1,2,"gray"))

BBEST documentation built on Jan. 8, 2021, 2:22 a.m.