filter: Filter a signal

Description

Generic filtering function. The default is to filter with an ARMA filter of given coefficients. The default filtering operation follows Matlab/Octave conventions.

Usage

# S3 method for default
filter(filt, a, x, init, init.x, init.y, ...)
# S3 method for Arma
filter(filt, x, ...)
# S3 method for Ma
filter(filt, x, ...)
# S3 method for Zpg
filter(filt, x, ...)

Value

The filtered signal, normally of the same length of the input signal x.

Arguments

filt: For the default case, the moving-average coefficients of an ARMA filter (normally called ‘b’). Generically, filt specifies an arbitrary filter operation.
a: the autoregressive (recursive) coefficients of an ARMA filter.
x: the input signal to be filtered.

init, init.x, init.y

init, init.x, init.y: allows to supply initial data for the filter - this allows to filter very large timeseries in pieces.
...: additional arguments (ignored).

Author

Tom Short, EPRI Solutions, Inc., (tshort@eprisolutions.com)

Details

The default filter is an ARMA filter defined as:

$a_{1} y_{n} + a_{2} y_{n - 1} + \dots + a_{n} y_{1} = b_{1} x_{n} + b_{2} x_{m - 1} + \dots + b_{m} x_{1}$

The default filter calls stats:::filter, so it returns a time-series object.

Since filter is generic, it can be extended to call other filter types.

References

https://en.wikipedia.org/wiki/Digital_filter

Octave Forge https://octave.sourceforge.io/

Examples

Run this code

bf <- butter(3, 0.1)                          # 10 Hz low-pass filter
t <- seq(0, 1, len = 100)                     # 1 second sample
x <- sin(2*pi*t*2.3) + 0.25*rnorm(length(t))  # 2.3 Hz sinusoid+noise
z <- filter(bf, x) # apply filter
plot(t, x, type = "l")
lines(t, z, col = "red")

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