require("akima", quietly = TRUE)

attach(mtcars)
par(mfrow=c(3,2))

numberCount = 100;
from = -2;
to = 2;
tau = 1;
a = 1;
m = 2;

h = 1;
xreal <- from + (0:100)*(to - from)/(100)
x <- from + (0:numberCount)*(to - from)/(numberCount)

discrete <- function(x, ap = a, taup = tau) ifelse(x <= taup/2, ifelse(x >= -taup/2, ap, 0), 0)
triangle <- function(x, ap = a, taup = tau) ifelse(x >= -taup/2,
                                                   ifelse(x <= taup/2,
                                                   ifelse(x <= 0, 2 * ap / taup * (x + taup / 2),
                                                   - 2 * ap / taup * (x - taup / 2)) , 0), 0);
sawtooth <- function(x, ap = a, taup = tau) ifelse(x >= -taup/2,
                                                   ifelse(x <= taup/2,
                                                          ifelse(x <= 0, 2 * ap * x / taup + ap,
                                                                 2 * ap * x / taup - ap), 0), 0);

gauss <- function(x, ap = a, taup = tau, mp = m) ap * exp(-(2*x/taup)^mp)

showGraphics <- function(func) {
  valuesreal <- func(xreal);
  values <- func(x)
  plot(xreal, valuesreal, type = c("p"), ylab = "y", xlab = "x", main = paste("Исходный график (поточечно)"), asp = 0.8);
  plot(xreal, valuesreal, type = c("l"), ylab = "y", xlab = "x", main = paste("Исходный график (линией)"), asp = 0.8);

  f <- fft(values);

  f2 = append(f, c(f[1]), after = length(f));

  realf <- Re(f);

  imaginef <- Im(f)

  barplot(Re(f2), xlab = paste("Real spectres"), main = paste("Действительная часть спектра"));
  barplot(Im(f2), xlab = paste("Im spectres"), main = paste("Мнимая часть спектра"));

  invrealf <- Re(fft(f, inverse = TRUE) / length(realf))

  hx <- c();
  hf <- c();

  for (i in 0:(numberCount + 1)) {
    if (h == 0 || i %% h == 0) {
      hx = append(hx, x[i], after = length(hx));
      hf = append(hf, f[i], after = length(hf));
    }
  }

  hinvf <- (fft(hf, inverse = TRUE) / length(hf));

  plot(hx, hinvf, type = c("p"), ylab = "y", xlab = "x", main = paste("Восстановленный график"), asp = 0.8, col = c("white"));
  #lines(spline(x = hx, y = hinvf, n = 10 * length(hx)), col = c("blue"))
  plot(hx, hinvf, type = c("l"), ylab = "y", xlab = "x", main = paste("Восстановленный график (линией)"));
}

showGraphics(gauss)