R: Filter a time-series

oceFilter {oce} | R Documentation

## Filter a time-series

### Description

Filter a time-series, possibly recursively

### Usage

    oceFilter(x, a = 1, b, zero.phase = FALSE)

### Arguments

`x` | a vector of numeric values, to be filtered as a time series.
`a` | a vector of numeric values, giving the a coefficients (see “Details”).
`b` | a vector of numeric values, giving the b coefficients (see “Details”).
`zero.phase` | boolean, set to `TRUE` to run the filter forwards, and then backwards, thus removing any phase shifts associated with the filter.

### Details

The filter is defined as e.g. y[i]=b[1]*x[i] + b[2]*x[i-1] + b[3]*x[i-2] + ... - a[2]*y[i-1] - a[3]*y[i-2] - a[4]*y[i-3] - ...y[i]=b[1]*x[i] + b[2]*x[i-1] + b[3]*x[i-2] + ... - a[2]*y[i-1] - a[3]*y[i-2] - a[4]*y[i-3] - ...y[i]=b[1]*x[i] + b[2]*x[i-1] + b[3]*x[i-2] + ... - a[2]*y[i-1] - a[3]*y[i-2] - a[4]*y[i-3] - ..., where some of the illustrated terms will be omitted if the lengths of `a` and `b` are too small, and terms are dropped at the start of the time series where the index on `x` would be less than 1.

By contrast with the `filter()` function of R, `oce.filter` lacks the option to do a circular filter. As a consequence, `oceFilter` introduces a phase lag. One way to remove this lag is to run the filter forwards and then backwards, as in the “Examples”. However, the result is still problematic, in the sense that applying it in the reverse order would yield a different result. (Matlab's `filtfilt` shares this problem.)

### Value

A numeric vector of the filtered results, y, as denoted in “Details”.

### Note

The first value in the `a` vector is ignored, and if `length(a)` equals 1, a non-recursive filter results.

### Author(s)

Dan Kelley

### Examples

    library(oce)
    par(mar=c(4, 4, 1, 1))
    b <- rep(1, 5)/5
    a <- 1
    x <- seq(0, 10)
    y <- ifelse(x == 5, 1, 0)
    f1 <- oceFilter(y, a, b)
    plot(x, y, ylim=c(-0, 1.5), pch="o", type='b')
    points(x, f1, pch="x", col="red")

    # remove the phase lag
    f2 <- oceFilter(y, a, b, TRUE)
    points(x, f2, pch="+", col="blue")

    legend("topleft", col=c("black","red","blue"), pch=c("o","x","+"),
           legend=c("data","normal filter", "zero-phase filter"))
    mtext("note that normal filter rolls off at end")

[Package oce version 1.2-0 Index]