# R functions to perform symmetric extension and
# periodization of a vector x, evaluated at index i

e11s <- function(x, i) {
 n<- length(x);
 period<- 2*n-2;      # WSS at 0 and WSS at n-1
 if(i<0) { i<- -i; }
 i<- i %% period;
 if(i>n-1) { i<- period-i; }
 return(x[i+1]);      # +1 accommodates index range 0,...,n-1.
}

e22s <- function(x, i) {
 n<- length(x);
 period<- 2*n-1;      # HSS at -1/2 and HSS at n-1/2
 if(i<0) { i<- -1-i; }
 i<- i %% period;
 if(i>n-1) { i<- period-i; }
 return(x[i+1]);      # +1 accommodates index range 0,...,n-1.
}

# example plots
indices <- 1:60;  shift <- 18;    # evaluate at -17,-16, ..., 42
u11s<-indices; u22s<-indices;     # initialize output vectors

u<-sin(2*pi*(1:9)/13);           # input: 9-sample vector

for(i in indices) {
  u11s[i] <- e11s(u,i-shift)
  u22s[i] <- e22s(u,i-shift)
}
matplot(cbind(u11s,u22s))