Digital Sound Processing

This post is one of a series of articles adapted from my university dissertation on data visualisation — see the rest of the series.

Recorded sound is taken in analogue form, converted to digital form and stored as binary. The decimal numeric representation of each of the samples can be used to process the sound, as they can be manipulated as matrices in MATLAB. For example the sound file numbers.wav stored as a row vector in MATLAB containing over 115,000 numeric values representing the samples making up the sounds. For example a random segment of the sound file:

-0.001617431640625
-0.000732421875000
-0.000976562500000
-0.000915527343750
-0.001831054687500
-0.001983642578125
0.000762939453125
0.000732421875000
-0.001403808593750
-0.000335693359375
0.001525878906250
0.002136230468750
0.000762939453125
-0.001159667968750
-0.000671386718750
-0.000488281250000
0.001556396484375
0.001190185546875
0.001586914062500
0.000915527343750
-0.000915527343750

which can be plotted to see the frequencies (plotted 100 samples either side):

The entire sound file looks like this:

I wrote a program to detect the start and end of each word spoken in the sound file, and created plots of each individual word:

The words are "Two", "One", "Four" and "Three". From here we can see how each of these words is spoken. The first actually seems to be made up of two separate sounds — this is because of the physical act of saying the two sounds "T" and "Ooh", which when slowed down, sound like there was a pause between them due to the change of oral position between sounds making up the word.

From these visual interpretations of the parts of the sounds we can study a sound file and see what is happening.

Another example of useful visualisation in digital sound is when applying a Fast Fourier Transform to a noisy sound file in order to locate the frequencies which are separate from the rest of the file. The file noiseysecret.dat contains a spoken sentence with noise laid over the top, making the voice inaudible. This is what the sound looks like with the noise:

Applying a Fast Fourier Transform to this noisy sound file allows us to pinpoint any abnormalities on a stem plot:

This shows us that the vast majority of the sound is towards zero on the scale of 0 to 1.4, but there is a definite inconsistency at around 1.1. Removing any values at this level will remove part of the noise from the sound. Let's see what it looks like after that's removed:

Now the scale has been restricted to 0.03, much lower than the previous plot, so we can see two other sets of inconsistencies. These too can be eradicated, leaving only the wanted part of the file — the spoken words (note the range of true sound values only goes up to 0.002):