# Parameters for an FIR filter from a Kaiser window Returns the parameters needed for fir1 to produce a filter of the desired specification from a Kaiser window. ```r kaiserord(f, m, dev, Fs = 2) ``` ## Arguments - `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 [0, 1], where 1 corresponds to the Nyquist frequency, Fs/2. ## Returns An object of class `FilterOfOrder` with the following list elements: - **n**: filter order - **Wc**: 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. [https://en.wikipedia.org/wiki/Kaiser_window](https://en.wikipedia.org/wiki/Kaiser_window) Octave Forge [https://octave.sourceforge.io/](https://octave.sourceforge.io/) ## Author(s) Original Octave version by Paul Kienzle pkienzle@users.sf.net . Conversion to R by Tom Short. ## See Also `hamming`, `kaiser` ## Examples ```r 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) ```

kaiserord function