# La rappresentazione grafica con R  di alcune serie di Fourier
dev.new(width=4,height=3); 
p <- function(x) {f <- 0;
  for(i in 0:n) f <- f+sin((2*i+1)*x)/(2*i+1); f <- f*4/pi}
n <- 1; plot(p,-5,10, ylim=c(-1.2,1.2), col="blue",n=1000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
n <- 2; plot(p,-5,10,add=TRUE,col="red",n=1000)
n <- 3; plot(p,-5,10,add=TRUE,col="green",n=1000)
#
dev.new(width=4,height=3); 
n <- 1000; plot(p,-5,10, ylim=c(-1.2,1.2), n=5000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
#
#
dev.new(width=4,height=3); 
p <- function(x) {f <- 0;
  for(i in 1:n) f <- f+sin((2*i)*x)/(2*i); f <- f*4/pi}
n <- 1; plot(p,-5,10, ylim=c(-1.5,1.5), col="blue",n=1000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
n <- 2; plot(p,-5,10,add=TRUE,col="red",n=1000)
n <- 3; plot(p,-5,10,add=TRUE,col="green4",n=1000)
#
dev.new(width=4,height=3); 
n <- 1000; plot(p,-5,10, ylim=c(-1.5,1.5), n=5000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
#
#
dev.new(width=4,height=3); 
p <- function(x) {f <- 0;
  for(i in 1:n) f <- f+sin((2*i+1)*x)/(2*i+1); f <- f*4/pi}
n <- 1; plot(p,-5,10, , ylim=c(-1.4,1.4), col="blue",n=1000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
n <- 2; plot(p,-5,10,add=TRUE,col="red",n=1000)
n <- 3; plot(p,-5,10,add=TRUE,col="green4",n=1000)
#
dev.new(width=4,height=3); 
n <- 1000; plot(p,-5,10, ylim=c(-1.4,1.4), n=5000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
#
#
dev.new(width=4,height=3); 
p <- function(x) {f <- pi^2/3;
   for(i in 1:n) f <- f+4*(-1)^i/i^2*cos(i*x); f};
n <- 1; plot(p,-5,10, ylim=c(-2,10),col="blue",n=1000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)
n <- 2; plot(p,-5,10,add=TRUE,col="red",n=1000)
n <- 3; plot(p,-5,10,add=TRUE,col="green4",n=1000)
n <- 4; plot(p,-5,10,add=TRUE,col="brown",n=1000)
#
dev.new(width=4,height=3); 
n <- 1000; plot(p,-5,10, ylim=c(-2,10), n=5000)
abline(h=0,v=0,lty=2,col="blue")
abline(v=axTicks(1), h=axTicks(2), col="grey",lty=3)