# Gammatone filter Generate gammatone filter in the time domain (impulse response). ```r 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: $$ g(t) = a \times t^{n-1} \times e^{-2\pi \beta t} \times \cos(2 \pi cf t + \phi)%g = a * t^{n-1} * e^{-2*pi*b*t} * cos(2*pi*f*t + p) $$ 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: $$ \beta = 24.7 \times (4.37 \times \frac{cf}{1000} + 1)%24.7*(4.37*cfreq/1000+1) $$ ## Returns A wave is returned. The class of the returned object is set with the argument `output`. ## 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. ## Author(s) Jerome Sueur ## Note Use the FFT based function, as `spec` or `meanspec`, to get the filter in the frequency domain. See examples. ## See Also `melfilterbank` ## Examples ```r ## 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) ```