kaiserord: Parameters for an FIR filter from a Kaiser window

Description

Returns the parameters needed for fir1 to produce a filter of the desired specification from a Kaiser window.

Usage

kaiserord(f, m, dev, Fs = 2)

Arguments

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.

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.

sampling rate. Used to convert the frequency specification into the [0, 1], where 1 corresponds to the Nyquist frequency, Fs/2.

Value

An object of class FilterOfOrder with the following list elements:

filter order

cutoff frequency

type

filter type, one of "low", "high", "stop", "pass", "DC-0", or "DC-1"

beta

shape parameter

References

Oppenheim, A. V., Schafer, R. W., and Buck, J. R. (1999). Discrete-time signal processing. Upper Saddle River, N.J.: Prentice Hall.

http://en.wikipedia.org/wiki/Kaiser_window

Octave Forge http://octave.sf.net

Examples

Run this code

# NOT RUN {
Fs <- 11025
op <- par(mfrow = c(2, 2), mar = c(3, 3, 1, 1))
for (i in 1:4) {
  switch(i,
    "1" = {
        bands <- c(1200, 1500)
        mag <- c(1, 0)
        dev <- c(0.1, 0.1)
    },
    "2" = {
        bands <- c(1000, 1500)
        mag <- c(0, 1)
        dev <- c(0.1, 0.1)
    },
    "3" = {
        bands <- c(1000, 1200, 3000, 3500)
        mag <- c(0, 1, 0)
        dev <- 0.1
    },
    "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)
  with(kaisprm, {
    d <<- max(1, trunc(n/10))
    if (mag[length(mag)]==1 && (d %% 2) == 1)
      d <<- d+1
    f1 <<- freqz(fir1(n, Wc, type, kaiser(n+1, beta), 'noscale'), 
        Fs = Fs)
    f2 <<- freqz(fir1(n-d, Wc, type, kaiser(n-d+1, beta), 'noscale'), 
        Fs = Fs)
  })                                                               
  plot(f1$f,abs(f1$h), col = "blue", type = "l", 
       xlab = "", ylab = "")
  lines(f2$f,abs(f2$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)
# }