Gammatone filter
Generate gammatone filter in the time domain (impulse response).
gammatone(f, d, cfreq, n = 4, a = 1, p = 0, output = "matrix")
f |
sampling frequency (in Hz). |
d |
duration (in s). |
cfreq |
center frequency (in Hz). |
n |
filter order (no unit). |
a |
amplitude (linear scale, no unit). |
p |
initial phase (in radians). |
output |
character string, the class of the object to return, either
|
The gammatone function in the time domain (impulse response) is
obtained with:
g = a * t^{n-1} * e^{-2*pi*b*t} * cos(2*pi*f*t + p)
with a the amplitude, t time, n the filter order, cf the center frequency, p the initial phase.
The parameter b is the equivalent rectangular
bandwidth (ERB) bandwidth which varies according to the center
frequency cf following:
24.7*(4.37*cfreq/1000+1)
A wave is returned. The class of the returned object is set with the argument output.
Jerome Sueur
Holdsworth J, Nimmo-Smith I, Patterson R, Rice P (1988) Implementing a gammatone filter bank. Annex C of the SVOS Final Report: Part A: The Auditory Filterbank, 1, 1-5.
## gammatone filter in the time domain (impulse response)
f <- 44100
d <- 0.05
res <- gammatone(f=f, d=d, cfreq=440, n=4)
## time display
oscillo(res, f=f)
## frequency display
spec(res, f=f)
## generate and plot a bank of 32 filters from 500 to 10000 Hz
n <- 32
cfreq <- round(seq(500, 10000, length.out=n))
res <- matrix(NA, nrow=f*d/2, ncol=n)
for(i in 1:n){
res[,i] <- spec(gammatone(f=f, d=d, cfreq=cfreq[i]), f=f, dB="max0", plot=FALSE)[,2]
}
x <- seq(0,f/2,length.out=nrow(res))/1000
plot(x=x, y=res[,1],
xlim=c(0,14), ylim=c(-60,0),
type="l", col=2, las=1,
xlab="Frequency (kHz)", ylab="Relative amplitude (dB)")
for(i in 2:n) lines(x, res[,i], col=2)
## use the frequency domain to filter a white noise input
## here around the center frequency 2000 Hz
res <- gammatone(f=f, d=d, cfreq=2000, n=4)
gspec <- spec(res, f=f, plot=FALSE)[,2]
nw <- noisew(f=44100, d=1)
nwfilt <- fir(nw, f=44100, wl=length(gspec)*2, custom=gspec)
spectro(nwfilt, f=f)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.