This page describes some basic sound processing functions in R. We'll use the sound package to read in wav files. No other packages will be needed for this tutorial, however there is a number of packages that are in general very useful for working with sound in R:

• signal - MATLAB like signal processing functions
• seewave - functions for analysing, manipulating, displaying, editing and synthesizing time waves (particularly sound).
• tuneR - collection of tools to analyze music, handling wave files, transcription.
We can install the `sound` package with
```  > install.packages('sound', dep=TRUE)
```
Assuming that the `sound` has already been installed correctly we can load it with the `library()` function
```  > library(sound)
```
Now we can read in a wav file, you can download it here 440_sine.wav it contains a complex tone with a 440 Hz fundamental frequency (F0) plus noise.

```
> sampFreq <- rate(sndSample)
> nBits <- bits(sndSample)
> snd <- sound(sndSample) # extract numerical values from sample object
```
the wav file has two channels and 5060 sample points

```  > dim(snd)
[1]    2 5060
```
considering the sample rate (sampFreq = 44110) this corresponds to about 114 ms duration
```  > 5060 / sampFreq
[1] 0.1147392
```
we'll select and work only with one of the channels from now onwards

``` > s1 <- snd[1,] ```

#### Plotting the Tone

A time representation of the sound can be obtained by plotting the pressure values against the time axis. However we need to create an array containing the time points first:

```  > timeArray <- (0:(5060-1)) / sampFreq
> timeArray <- timeArray * 1000
```
now we can plot the tone

``` > plot(timeArray, s1, type='l', col='black', xlab='Time (ms)', ylab='Amplitude') ```

#### Plotting the Frequency Content

Another useful graphical representation is that of the frequency content of the tone. We can obtain the frequency content of the sound using the ` fft ` function, that implements a Fast Fourier Transform algorithm. We'll follow closely the following technical document http://www.mathworks.com/support/tech-notes/1700/1702.html to obtain the power spectrum of our sound.

```  n <- length(s1)
p <- fft(s1)
```
the `fft` is computed on the number of points of the signal (n). Since we're not using a power of two the computation will be a bit slower, but for signals of this duration this is negligible.
```  nUniquePts <- ceiling((n+1)/2)
p <- p[1:nUniquePts] #select just the first half since the second half
# is a mirror image of the first
p <- abs(p)  #take the absolute value, or the magnitude
```
the fourier transform of the tone returned by the `fft` function contains both magnitude and phase information and is given in a complex representation (i.e. returns complex numbers). By taking the absolute value of the fourier transform we get the information about the magnitude of the frequency components.
```
p <- p / n #scale by the number of points so that
# the magnitude does not depend on the length
# of the signal or on its sampling frequency
p <- p^2  # square it to get the power

# multiply by two (see technical document for details)
# odd nfft excludes Nyquist point
if (n %% 2 > 0){
p[2:length(p)] <- p[2:length(p)]*2 # we've got odd number of points fft
} else {
p[2: (length(p) -1)] <- p[2: (length(p) -1)]*2 # we've got even number of points fft
}

freqArray <- (0:(nUniquePts-1)) * (sampFreq / n) #  create the frequency array

plot(freqArray/1000, 10*log10(p), type='l', col='black', xlab='Frequency (kHz)', ylab='Power (dB)')
```
The resulting plot can bee seen below, notice that we're plotting the power in decibels by taking `10*log10(p)`, we're also scaling the frequency array to kilohertz by dividing it by 1000

To confirm that the value we have computed is indeed the power of the signal, we'll also compute the root mean square (rms) of the signal. Loosely speaking the rms can be seen as a measure of the amplitude of a waveform. If you just took the average amplitude of a sinusoidal signal oscillating around zero, it would be zero since the negative parts would cancel out the positive parts. To get around this problem you can square the amplitude values before averaging, and then take the square root (notice that squaring also gives more weight to the extreme amplitude values):
```  > rms_val <- sqrt(mean(s1^2))
> rms_val
[1] 0.06150006
```
since the rms is equal to the square root of the overall power of the signal, summing the power values calculated previously with the `fft` over all frequencies and taking the square root of this sum should give a very similar value
```  > sqrt(sum(p))
[1] 0.06150006
```