Second-order sections filtering
One-dimensional second-order (biquadratic) sections IIR digital filtering.
sosfilt(sos, x, zi = NULL)
sos |
Second-order section representation, specified as an nrow-by-6
matrix, whose rows contain the numerator and denominator coefficients of
the second-order sections: |
x |
the input signal to be filtered, specified as a vector or as a
matrix. If |
zi |
If |
The filter function is implemented as a series of second-order filters with direct-form II transposed structure. It is designed to minimize numerical precision errors for high-order filters [1].
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.
Smith III, J.O. (2012). Introduction to digital filters, with audio applications (3rd Ed.). W3K Publishing.
fs <- 1000
t <- seq(0, 1, 1/fs)
s <- sin(2* pi * t * 6)
x <- s + rnorm(length(t))
plot(t, x, type = "l", col="light gray")
lines(t, s, col="black")
sosg <- butter(3, 0.02, output = "Sos")
sos <- sosg$sos
sos[1, 1:3] <- sos[1, 1:3] * sosg$g
y <- sosfilt(matrix(sos, ncol=6), x)
lines(t, y, col="red")
## using 'filter' will handle the gain for you
y2 <- filter(sosg, x)
all.equal(y, y2)
## The following example is from Python scipy.signal.sosfilt
## It shows the instability that results from trying to do a
## 13th-order filter in a single stage (the numerical error
## pushes some poles outside of the unit circle)
arma <- ellip(13, 0.009, 80, 0.05, output='Arma')
sos <- ellip(13, 0.009, 80, 0.05, output='Sos')
x <- rep(0, 700); x[1] <- 1
y_arma <- filter(arma, x)
y_sos <- filter(sos, x)
plot(y_arma, type ="l")
lines (y_sos, col = 2)
legend("topleft", legend = c("Arma", "Sos"), lty = 1, col = 1:2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.