gammatone: Gammatone filter

Description

Generate gammatone filter in the time domain (impulse response).

Usage

gammatone(f, d, cfreq, n = 4, a = 1, p = 0, output = "matrix")

Value

A wave is returned. The class of the returned object is set with the argument output.

Arguments

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 "matrix", "Wave", "Sample", "audioSample" or "ts".

Author

Jerome Sueur

Details

The gammatone function in the time domain (impulse response) is obtained with:
$g (t) = a \times t^{n - 1} \times e^{- 2 π β t} \times \cos (2 π c f t + ϕ)$ with a the amplitude, t time, n the filter order, cf the center frequency, $ϕ$ the initial phase.
The parameter $β$ is the equivalent rectangular bandwidth (ERB) bandwidth which varies according to the center frequency $c f$ following:
$β = 24.7 \times (4.37 \times \frac{c f}{1000} + 1)$

References

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.

Examples

Run this code

## 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)

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