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```
## Copyright (C) 2000 Paul Kienzle
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## usage: b = fir1(n, w [, type] [, window] [, noscale])
##
## Produce an order n FIR filter with the given frequency cutoff,
## returning the n+1 filter coefficients in b.
##
## n: order of the filter (1 less than the length of the filter)
## w: band edges
## strictly increasing vector in range [0, 1]
## singleton for highpass or lowpass, vector pair for bandpass or
## bandstop, or vector for alternating pass/stop filter.
## type: choose between pass and stop bands
## 'high' for highpass filter, cutoff at w
## 'stop' for bandstop filter, edges at w = [lo, hi]
## 'DC-0' for bandstop as first band of multiband filter
## 'DC-1' for bandpass as first band of multiband filter
## window: smoothing window
## defaults to hamming(n+1) row vector
## returned filter is the same shape as the smoothing window
## noscale: choose whether to normalize or not
## 'scale': set the magnitude of the center of the first passband to 1
## 'noscale': don't normalize
##
## To apply the filter, use the return vector b:
## y=filter(b,1,x)
##
## Examples:
## freqz(fir1(40,0.3))
## freqz(fir1(15,[0.2, 0.5], 'stop')); # note the zero-crossing at 0.1
## freqz(fir1(15,[0.2, 0.5], 'stop', 'noscale'))
## TODO: Consider using exact expression (in terms of sinc) for the
## TODO: impulse response rather than relying on fir2.
## TODO: Find reference to the requirement that order be even for
## TODO: filters that end high. Figure out what to do with the
## TODO: window in these cases
fir1 <- function(n, w, type = c("low", "high", "stop", "pass", "DC-0", "DC-1"),
window = hamming(n+1), scale = TRUE) {
type <- match.arg(type)
if (!is.logical(scale)) {
scale <- match.arg(scale, c("scale", "noscale"))
scale <- scale == "scale"
}
if(is.function(window))
window <- window(n+1)
else if(is.character(window))
window <- do.call(window, list(n+1))
## Assign default window, filter type and scale.
## If single band edge, the first band defaults to a pass band to
## create a lowpass filter. If multiple band edges, the first band
## defaults to a stop band so that the two band case defaults to a
## band pass filter. Ick.
ftype <- tolower(type) %in% c('low','stop','dc-1')
## build response function according to fir2 requirements
bands <- length(w) + 1
f <- numeric(2*bands)
f[2*bands] = 1
f[seq(2, 2*bands-1, by = 2)] <- w
f[seq(3, 2*bands-1, by = 2)] <- w
m <- numeric(2*bands)
m[seq(1, 2*bands, by = 2)] <- (1:bands - (1-ftype)) %% 2
m[seq(2, 2*bands, by = 2)] <- m[seq(1, 2*bands, by = 2)]
## Increment the order if the final band is a pass band. Something
## about having a nyquist frequency of zero causing problems.
if (n %% 2 == 1 && m[2*bands] == 1) {
warning("n must be even for highpass and bandstop filters. Incrementing.")
n <- n + 1
if (is.vector(window) && is.double(window)) {
## End the window using interpolation
M <- length(window)
if (M == 1)
window <- c(window, window)
else
window <- interp1(seq(0,1,length=M), window, seq(0,1,length=M+1),
if (M < 4) 'linear' else 'spline')
}
}
## compute the filter
b <- fir2(n, f, m, 512, 2, window)
## normalize filter magnitude
if (scale) {
## find the middle of the first band edge
if (m[1] == 1)
w_o <- (f[2] - f[1])/2
else
w_o <- f[3] + (f[4] - f[3])/2
## compute |h(w_o)|^-1
renorm <- 1/abs(polyval(b, exp(-1i*pi*w_o)))
## normalize the filter
b <- renorm*b
}
Ma(b)
}
#!demo
#! freqz(fir1(40,0.3))
#!demo
#! freqz(fir1(15,[0.2, 0.5], 'stop')); # note the zero-crossing at 0.1
#!demo
#! freqz(fir1(15,[0.2, 0.5], 'stop', 'noscale'))
#!assert(fir1(2, .5, 'low', @hanning, 'scale'), [0 1 0]')
#!assert(fir1(2, .5, 'low', "hanning", 'scale'), [0 1 0]')
#!assert(fir1(2, .5, 'low', hamming(3), 'scale'), [0 1 0]')
#!assert(fir1(10,.5,'noscale'), fir1(10,.5,'low','hamming','noscale'))
#!assert(fir1(10,.5,'high'), fir1(10,.5,'high','hamming','scale'))
#!assert(fir1(10,.5,'boxcar'), fir1(10,.5,'low','boxcar','scale'))
#!assert(fir1(10,.5,'hanning','scale'), fir1(10,.5,'scale','hanning','low'))
#!assert(fir1(10,.5,'haNNing','NOscale'), fir1(10,.5,'noscale','Hanning','LOW'))
#!assert(fir1(10,.5,'boxcar',[]), fir1(10,.5,'boxcar'))
```

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