Kaiser filter order and cutoff frequency
Return the parameters needed to produce a FIR filter of the desired specification from a Kaiser window.
kaiserord(f, m, dev, fs = 2)
f |
frequency bands, given as pairs, with the first half of the first pair assumed to start at 0 and the last half of the last pair assumed to end at 1. It is important to separate the band edges, since narrow transition regions require large order filters. |
m |
magnitude within each band. Should be non-zero for pass band and zero for stop band. All passbands must have the same magnitude, or you will get the error that pass and stop bands must be strictly alternating. |
dev |
deviation within each band. Since all bands in the resulting filter have the same deviation, only the minimum deviation is used. In this version, a single scalar will work just as well. |
fs |
sampling rate. Used to convert the frequency specification into the
c(0, 1) range, where 1 corresponds to the Nyquist frequency, |
Given a set of specifications in the frequency domain, kaiserord
estimates the minimum FIR filter order that will approximately meet the
specifications. kaiserord converts the given filter specifications
into passband and stopband ripples and converts cutoff frequencies into the
form needed for windowed FIR filter design.
kaiserord uses empirically derived formulas for estimating the orders
of lowpass filters, as well as differentiators and Hilbert transformers.
Estimates for multiband filters (such as band-pass filters) are derived from
the low-pass design formulas.
The design formulas that underlie the Kaiser window and its application to FIR filter design are
β =
0.1102(α - 8.7), α > 50
0.5842(α -21)^{0.4} + 0.07886(α - 21), 21 ≤ α ≤ 50
0, α < 21
where α = -20log_{10}(δ) is the stopband attenuation expressed in decibels, n=(α - 8) / 2.285(Δω), where n is the filter order and Δω is the width of the smallest transition region.
A list of class FilterSpecs with the following list
elements:
filter order
cutoff frequency
filter type, one of "low", "high", "stop", "pass", "DC-0", or "DC-1".
shape parameter
Paul Kienzle.
Conversion to R by Tom Short,
adapted by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
fs <- 11025
op <- par(mfrow = c(2, 2), mar = c(3, 3, 1, 1))
for (i in 1:4) {
if (i == 1) {
bands <- c(1200, 1500)
mag <- c(1, 0)
dev <- c(0.1, 0.1)
}
if (i == 2) {
bands <- c(1000, 1500)
mag <- c(0, 1)
dev <- c(0.1, 0.1)
}
if (i == 3) {
bands <- c(1000, 1200, 3000, 3500)
mag <- c(0, 1, 0)
dev <- 0.1
}
if (i == 4) {
bands <- 100 * c(10, 13, 15, 20, 30, 33, 35, 40)
mag <- c(1, 0, 1, 0, 1)
dev <- 0.05
}
kaisprm <- kaiserord(bands, mag, dev, fs)
d <- max(1, trunc(kaisprm$n / 10))
if (mag[length(mag)] == 1 && (d %% 2) == 1) {
d <- d + 1
}
f1 <- freqz(fir1(kaisprm$n, kaisprm$Wc, kaisprm$type,
kaiser(kaisprm$n + 1, kaisprm$beta),
scale = FALSE),
fs = fs)
f2 <- freqz(fir1(kaisprm$n - d, kaisprm$Wc, kaisprm$type,
kaiser(kaisprm$n - d + 1, kaisprm$beta),
scale = FALSE),
fs = fs)
plot(f1$w, abs(f1$h), col = "blue", type = "l", xlab = "", ylab = "")
lines(f2$w, abs(f2$h), col = "red")
legend("right", paste("order", c(kaisprm$n-d, kaisprm$n)),
col = c("red", "blue"), lty = 1, bty = "n")
b <- c(0, bands, fs/2)
for (i in seq(2, length(b), by=2)) {
hi <- mag[i/2] + dev[1]
lo <- max(mag[i/2] - dev[1], 0)
lines(c(b[i-1], b[i], b[i], b[i-1], b[i-1]), c(hi, hi, lo, lo, hi))
}
}
par(op)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.