gammatone: Gammatone filter

In seewave: Sound Analysis and Synthesis

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".

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)

Value

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

Note

Use the FFT based function, as spec or meanspec, to get the filter in the frequency domain. See examples.

Author(s)

Jerome Sueur

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

## 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)

seewave documentation built on Oct. 19, 2023, 5:07 p.m.