# Difference between two frequency spectra This function estimates the surface difference between two frequency spectra. ```r diffspec(spec1, spec2, f = NULL, mel = FALSE, plot = FALSE, type="l", lty=c(1, 2), col =c(2, 4, 8), flab = NULL, alab = "Amplitude", flim = NULL, alim = NULL, title = TRUE, legend = TRUE, ...) ``` ## Arguments - `spec1`: a first data set resulting of a spectral analysis obtained with `spec` or `meanspec` (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude). - `spec2`: a first data set resulting of a spectral analysis obtained with `spec` or `meanspec` (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude). - `f`: sampling frequency of waves used to obtain `spec1` and `spec2` (in Hz). Not necessary if `spec1` and/or `spec2` is a two-column matrix obtained with `spec` or `meanspec`. - `mel`: a logical, if `TRUE` the (htk-)mel scale is used. - `plot`: logical, if `TRUE` plots both spectra and their surface difference (by default `FALSE`). - `type`: if `plot` is `TRUE`, type of plot that should be drawn. See `plot` for details (by default "l" for lines). - `lty`: a vector of length 2 for the line type of `spec1` and `spec2` if `type`="l". - `col`: a vector of length 3 for the colour of `spec1`, `spec2`, and the surface difference between each of them. - `flab`: title of the frequency axis. - `alab`: title of the amplitude axis. - `flim`: the range of frequency values. - `alim`: range of amplitude axis. - `title`: logical, if `TRUE`, adds a title with D value. - `legend`: logical, if `TRUE` adds a legend to the plot. - ``...``: other `plot` graphical parameters. ## Details D is a Manhattan distance (l1 norm). Both spectra are first transformed as probability mass functions (PMF). Spectral difference is then computed according to: $$ D = \frac{\sum{|spec1-spec2|}}{2}, with D \in [0,1].%D = sum(abs(spec1-spec2))/2 $$ , with 0 < D < 1. ## Returns The difference is returned. This value is without unit. When `plot` is `TRUE`, both spectra and their difference surface are plotted on the same graph. ## References Sueur, J., Pavoine, S., Hamerlynck, O. and Duvail, S. (2008). Rapid acoustic survey for biodiversity appraisal. **PLoS One**, 3(12): e4065. ## Author(s) Jerome Sueur, Sandrine Pavoine and Laurent Lellouch ## Note This method can be used as a relative distance estimation between different spectra. The dB value obtained can be very different from the one visually estimated when looking at the graph (`plot=TRUE`). ## See Also `spec`, `meanspec`, `corspec`, `simspec`, `diffcumspec`, `diffenv`, `kl.dist`, `ks.dist`, `logspec.dist`, `itakura.dist` ## Examples ```r a <- noisew(f=8000,d=1) b <- synth(f=8000,d=1,cf=2000) c <- synth(f=8000,d=1,cf=1000) d <- noisew(f=8000,d=1) speca <- spec(a,f=8000,wl=512,at=0.5,plot=FALSE) specb <- spec(b,f=8000,wl=512,at=0.5,plot=FALSE) specc <- spec(c,f=8000,wl=512,at=0.5,plot=FALSE) specd <- spec(d,f=8000,wl=512,at=0.5,plot=FALSE) diffspec(speca,speca,f=8000) #[1] 0 => similar spectra of course ! diffspec(speca,specb) diffspec(speca,specc,plot=TRUE) diffspec(specb,specc,plot=TRUE) diffspec(speca,specd,plot=TRUE) ## mel scale require(tuneR) data(orni) data(tico) orni.mel <- melfcc(orni, nbands = 256, dcttype = "t3", fbtype = "htkmel", spec_out=TRUE) orni.mel.mean <- apply(orni.mel$aspectrum, MARGIN=2, FUN=mean) tico.mel <- melfcc(tico, nbands = 256, dcttype = "t3", fbtype = "htkmel", spec_out=TRUE) tico.mel.mean <- apply(tico.mel$aspectrum, MARGIN=2, FUN=mean) diffspec(orni.mel.mean, tico.mel.mean, f=22050, mel=TRUE, plot=TRUE) ```

diffspec function