seewave (version 2.1.6)

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")

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".

Value

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

Details

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

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.

See Also

melfilterbank

Examples

# NOT RUN {
## 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)
# }