Filter a signal
Apply a 1-D digital filter compatible with 'Matlab' and 'Octave'.
filter(filt, ...) ## Default S3 method: filter(filt, a, x, zi = NULL, ...) ## S3 method for class 'Arma' filter(filt, x, ...) ## S3 method for class 'Ma' filter(filt, x, ...) ## S3 method for class 'Sos' filter(filt, x, ...) ## S3 method for class 'Zpg' filter(filt, x, ...) ## S3 method for class 'Zpg' filter(filt, x, ...)
filt |
For the default case, the moving-average coefficients of an ARMA
filter (normally called ‘b’), specified as a vector. Generically,
|
... |
additional arguments (ignored). |
a |
the autoregressive (recursive) coefficients of an ARMA filter,
specified as a vector. If |
x |
the input signal to be filtered, specified as a vector or as a
matrix. If |
zi |
If |
The filter is a direct form II transposed implementation of the standard linear time-invariant difference equation:
N M SUM a(k+1)y(n-k) + SUM b(k+1)x(n-k) = 0; 1 <= n <= length(x) k=0 k=0
where N = length(a) - 1 and M = length(b) - 1.
The initial and final conditions for filter delays can be used to filter data in sections, especially if memory limitations are a consideration. See the examples.
The filtered signal, of the same dimensions as the input signal. In
case the zi input argument was specified, a list with two elements
is returned containing the variables y, which represents the output
signal, and zf, which contains the final state vector or matrix.
Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
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")
## specify initial conditions
## from Python scipy.signal.lfilter() documentation
t <- seq(-1, 1, length.out = 201)
x <- (sin(2 * pi * 0.75 * t * (1 - t) + 2.1)
+ 0.1 * sin(2 * pi * 1.25 * t + 1)
+ 0.18 * cos(2 * pi * 3.85 * t))
h <- butter(3, 0.05)
lab <- max(length(h$b), length(h$a)) - 1
zi <- filtic(h$b, h$a, rep(1, lab), rep(1, lab))
z1 <- filter(h, x)
z2 <- filter(h, x, zi * x[1])
plot(t, x, type = "l")
lines(t, z1, col = "red")
lines(t, z2$y, col = "green")
legend("bottomright", legend = c("Original signal",
"Filtered without initial conditions",
"Filtered with initial conditions"),
lty = 1, col = c("black", "red", "green"))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.