Measures of acoustic structure

Spectrographic parameters

The specan() function measures the following spectrographic parameters related to amplitude distributions in time and frequency, descriptors of the fundamental and dominant frequency contours and descriptors of harmonic content:

We can easily measure them as follows:

library(warbleR)

# load examples
data("lbh_selec_table")

# global parameters
warbleR_options(wav.path = "./examples", flim = c(1, 10), wl = 200, ovlp = 90, pb = FALSE)

sp <- specan(lbh_selec_table)

sp

Statistical descriptors of cepstral coefficients

These coefficients were designed to decompose the sounds in a similar way than the human auditory system in order to facilitate speech recognition. The central idea is to compress the acoustic data maintaining only relevant information for the detection of phonetic differences. The principle refers to human hearing using the Mel logarithmic scale whose definition is based on how the human ear perceives frequency and loudness (Sueur 2018). Cepstral coefficients are literally defined as “the result of a cosine transformation of the real logarithm of short-term energy spectra expressed on a Mel frequency scale”.

The descriptive statistics that are extracted from the cepstral coefficients are: minimum, maximum, average, median, asymmetry, kurtosis and variance. It also returns the mean and variance for the first and second derivatives of the coefficients. These parameters are commonly used in the processing and detection of acoustic signals (e.g. Salamon et al 2014). They have been widely used for human voice analysis and its use has extended to mammalian bioacoustics, although they also appear to be useful for quantifying the structure of acoustic signals in other groups.

In warbleR we can calculate statistical descriptors of cepstral coefficients with the mfcc_stats() function:

cc <- mfcc_stats(X = lbh_selec_table)

cc

(Spectrographic) cross correlation

This analysis correlates the amplitude values in the frequency and time space pairwise for all signals in a selection table. The correlation represents a measure of spectrographic similarity of the signals:

xcor <- x_corr(X = lbh_selec_table)

xcor

Dynamic time warping

In time series analysis, time dynamics distortion (DTW) is one of the algorithms to measure the similarity between two time sequences, which may vary in their ‘speed’. The sequences are nonlinearly ‘warped’ in the temporal dimension to determine a measure of their similarity independent of certain nonlinear variations in the temporal dimension.

The dfDTW() function extracts the dominant frequency values as a time series and then calculates the acoustic dissimilarity using dynamic time warping. The function uses the approx() function to interpolate values between the dominant frequency measurements:

dtwdist <- df_DTW(lbh_selec_table)

The function returns a matrix with paired dissimilarity values.

If img = TRUE, the function also produces image files with the spectrograms of the signals listed in the input data frame that shows the location of the dominant frequencies.

df_DTW(lbh_selec_table, img = TRUE, col = "red", pch = 21, line = FALSE)

Frequency contours can be calculated independently using the df_ts() function. These contours can be adjusted manually with the sel_tailor() function.

download.file(url = "https://ndownloader.figshare.com/files/21167052", 
 destfile = "iniquiry_calls.RDS")

#function to create group membership binary matrix
bi_mats <- function(X, labels) {
  
  # create empty matrix to store memebership matrix
  mat <- matrix(nrow = ncol(X), ncol = ncol(X))
 
  # add labels to row and col names
  rownames(mat) <- colnames(mat) <- labels
  
  # add 0 if same lek and 1 if else 
  out <- lapply(1:(length(labels) - 1), function(i){
  sapply((i + 1):length(labels), function(j) 
    if (labels[i] == labels[j]) 0 else 1)  
    })

  # add to mat
  mat[lower.tri(mat)] <- unlist(out)

  # retunr as distance matrix
  return(as.dist(mat))
  }

Additional measures

snr <- sig2noise(X = lbh_selec_table, mar = 0.06)

snr

cntrs <- df_ts(X = lbh_selec_table)

inflcts <- inflections(cntrs)

# add a 'song' column
lbh_selec_table$song <- rep(1:4, each = 3)[1:11]

# measure default parameters
song_param(X = lbh_selec_table, song_colm = "song", parallel = 1, pb = TRUE)

# measure acoustic parameters
sp <- specan(lbh_selec_table[1:8, ], bp = c(1, 11), 300, fast = TRUE)

sp <- merge(sp, lbh_selec_table[1:8, ], by = c("sound.files", "selec"))

# caculate song-level parameters for all numeric parameters
song_param(X = sp, song_colm = "song", parallel = 1, pb = TRUE)

# caculate song-level parameters selecting parameters with mean_colm
song_param(X = sp, song_colm = "song",mean_colm = c("dfrange", "duration"), parallel = 1, pb = TRUE)

song_param(X = sp, weight = "duration", song_colm = "song",
mean_colm =  c("dfrange", "duration"), min_colm =  "mindom", max_colm = "maxdom", 
  parallel = 1, pb = TRUE)

download.file(url = "https://ndownloader.figshare.com/files/21189891", 
 destfile = "response_calls.RDS")

References

1. Araya-Salas M, Smith-Vidaurre G (2017) warbleR: An R package to streamline analysis of animal acoustic signals. Methods Ecol Evol 8:184–191.

2. Lyon, R. H., & Ordubadi, A. (1982). Use of cepstra in acoustical signal analysis. Journal of Mechanical Design, 104(2), 303-306.

3. Salamon, J., Jacoby, C., & Bello, J. P. (2014). A dataset and taxonomy for urban sound research. In Proceedings of the 22nd ACM international conference on Multimedi. 1041-1044.

Session information

## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=es_CR.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=es_CR.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=es_CR.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=es_CR.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] kableExtra_1.1.0   warbleR_1.1.24     NatureSounds_1.0.3 knitr_1.29        
## [5] seewave_2.1.6      tuneR_1.3.3       
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.4.6      highr_0.8         compiler_3.6.3    pillar_1.4.4     
##  [5] Sim.DiffProc_4.6  bitops_1.0-6      tools_3.6.3       digest_0.6.25    
##  [9] viridisLite_0.3.0 evaluate_0.14     tibble_3.0.1      lifecycle_0.2.0  
## [13] fftw_1.0-6        pkgconfig_2.0.3   rlang_0.4.6       rstudioapi_0.11  
## [17] yaml_2.2.1        parallel_3.6.3    xfun_0.15         xml2_1.3.2       
## [21] httr_1.4.1        stringr_1.4.0     vctrs_0.3.0       hms_0.5.3        
## [25] webshot_0.5.2     glue_1.4.1        R6_2.4.1          dtw_1.21-3       
## [29] pbapply_1.4-2     rmarkdown_2.1     readr_1.3.1       magrittr_1.5     
## [33] scales_1.1.1      htmltools_0.4.0   ellipsis_0.3.1    MASS_7.3-51.5    
## [37] rvest_0.3.5       colorspace_1.4-1  Deriv_4.0         stringi_1.4.6    
## [41] proxy_0.4-24      munsell_0.5.0     signal_0.7-6      RCurl_1.98-1.2   
## [45] crayon_1.3.4      rjson_0.2.20