# Simple Causal Moving Average of length n wit zero padding
simpleCMA <- function(x, n)
{
  y <- numeric(length(x))
  for (i in 1:length(x))
  {
    sum <- 0
    for (j in (0:(n-1)))
    {
      if (i - j > 0)
      {
        sum <- sum + x[i-j]
      }
    }
    y[i] <- sum/n
  }
  return(y)
}

# Causal Moving Average of length n with zero padding
filterCMA <- function(x, n)
{
  res <- numeric(n)
  for(i in 1:length(x)){
    res[i] <- sum(x[(max(i-(n-1),1)):i])/n
  }
  res
}

# Moving Average of length n with zero padding
filterMA <- function(x, n)
{
  res <- numeric(n)
  for(i in 1:length(x))
  {
    res[i] <- sum(x[(max(i-floor(n/2),1)):(min(i+floor(n/2),length(x)))])/n
  }
  return(res)
}

# Moving Average from i-M1 to i+M2 with zero padding
filterMA_M1M2 <- function(x, M1, M2)
{
  res <- numeric(n)
  for(i in 1:length(x))
  {
    res[i] <- sum(x[(max(i-M1,1)):(min(i+M2,length(x)))])/n
  }
  return(res)
}

# Causal Weighted Moving Average for coefficients b with zero padding (conv(x,b))
filterCWMA <- function(x, b)
{
  res <- numeric(length(b))
  for(i in 1:length(x))
  {
    if (i < length(b))
    {
      res[i] <- sum(rev(b[1:i])*x[1:i])
    }
    else
    {
      res[i] <- sum(rev(b)*x[(i-(length(b)-1)):i])
    }
  }
  return(res)
}

# Weighted Moving Average for coefficients b with zero padding
filterWMA <- function(x, b)
{
  res <- numeric(length(b))
  back <- ceiling((length(b)-1)/2)
  forw <- floor((length(b)-1)/2)
  for(i in 1:length(x))
  {
    if (i < back + 1)
    {
      res[i] <- sum(rev(b[1:(i+forw)])*x[1:(i+forw)])
    }
    else if (i > length(x) - forw)
    {
      res[i] <- sum(rev(b[(i-(length(x)-forw-1)):length(b)])*x[((i-back):(i+forw-(i-(length(x)-forw))))])
    }
    else
    {
      res[i] <- sum(rev(b)*x[((i-back):(i+forw))])      
    }
  }
  return(res)
}