R: How to generate a noisy sine function

Question

I am still pretty new to the whole R-thing.

I have the following aim; I have a sine function that describes a calcium particle number over time: something like y = a * sin (b*t) + c

Since in reality the generation and removal of calcium is described in stochastic events, I would like to add a random noise term to my function (preferably scalable in average noise amplitude).

Something like z = y + random*Amplitude

can you help me out?

Best

Blighter

Answer 1

Here's an approach I would use - I provided two options on how your error might be generated (uniform distribution vs Gaussian distribution):

### Equation: y=a*sin(b*t)+c.unif*amp
# variables
n <- 100 # number of data points
t <- seq(0,4*pi,,100)
a <- 3
b <- 2
c.unif <- runif(n)
c.norm <- rnorm(n)
amp <- 2

# generate data and calculate "y"
set.seed(1)
y1 <- a*sin(b*t)+c.unif*amp # uniform error
y2 <- a*sin(b*t)+c.norm*amp # Gaussian/normal error

# plot results
plot(t, y1, t="l", ylim=range(y1,y2)*c(1,1.2))
lines(t, y2, col=2)
legend("top", legend=c("y1", "y2"), col=1:2, lty=1, ncol=2, bty="n")

Howe

Answer 2

y <- jitter(a*sin(b*t) + c) using the jitter() function will add random noise to your function. you can specify the "amount" parameter inside jitter() to control the amplitude.

Deicer

Isn't jitter() intended to small noise just for the purpose of visualization (avoiding repeated datapoints to obscure each other)? – Socrates

not familiar with jitter but it is not working as shown above in any case giving Error in a * b + c : non-numeric argument to binary operator – Keitt

You don't need the +c part any more, ie just jitter(asin(bt)) - if you remove that @javadba it will work. – Testudo

Thx @NickCotter – Keitt