T<-300
X <- array(rnorm(T), T)
plot(X,t='l')

C <- cos(2*pi*(1:T)/50)
Y <- X+C
plot(C)
plot(Y)

S <- lowess(Y,f=0.1)$y
S <- (S-mean(S))/sd(S)
plot(S)

## For the cosine term alone
DFTmagnitude <- abs(fft(C))
plot(DFTmagnitude[1:150],t='l') 
which.max(DFTmagnitude[1:150])

## For the noise plus the cosine term
DFTmagnitude <- abs(fft(Y))
plot(DFTmagnitude[1:150],t='l') 
which.max(DFTmagnitude[1:150])

## For the smoothed noise and cosine
DFTmagnitude <- abs(fft(S))
plot(DFTmagnitude[1:150],t='l') 
which.max(DFTmagnitude[1:150])

Z <- Y
Z[100:110] <- Z[100:110]+1
plot(Z)

S <- lowess(Z,f=0.1)$y
plot(S)

n <- 20
T <- 300
X <- array(rnorm(n*T),c(n,T))
X[1:10, 100:110] <- X[1:10, 100:110] + 1