## An Attempt of Denoising with Matlab

We discuss some examples of discrete denoising filters against the Vuvuzela noise

in recordings of soccer games during the World-Cup 2010 in South-Africa and listen to the corresponding denoising effects.

We implement a discrete 2nd order notch and a discrete 3rd order Butterworth lowpass filter.

The notch filter is repeatedly used to eliminate several noise frequencies.

The notches in the frequency response of the filters are chosen for example at the Vuvuzela frequencies

233 Hz, 466 Hz (Octave), 699 Hz (Quint) and 932 Hz (Octave).

With a Butterworth lowpass cutoff frequency at 2000 Hz and dc-gain 2 (to get back signal energy lost by filtering),

that type of “Anti-Vuvuzela-Filtering” has results as in the following examples, when you download and test the m-Files:

Original Recording 1 with Vuvuzela Noise

Original Recording 2 with Vuvuzela Noise

Filtered Version of Recording 1

Filtered Version of Recording 2

The filters are realized with the following m-files

A demo m-file that realizes the filtering difference equations for a recording with Vuvuzela noise

m-file, that computes the coefficients of a 2nd order discrete notch filter

m-file, that computes the output the notch filter

m-file, that computes the output of a 3rd order IIR filter

m-file, that computes a 3rd order Butterworth filter

m-file, that computes a vector of complex exponentials at sampling frequencies

The absolute amplitude distortions of the filters with the lowpass cutoff frequency at 2000 Hz is shown in the following figure

Students could proceed with an application of the built in Matlab filter function in a similar test and compare, by writing and applying a discrete parametric equalizer instead of a notch filter or by writing for tests more sophisticated denoising algorithms like time-frequency block-thresholding or wavelet methods with adaptive block attenuation. We talk on those methods and their mathematical requisites in our lessons. You can also easily find many articles on the denoising problem asking a search machine. An overview on

image denoising is given in **Sciencedirect**. Acoustic denoising is difficult work and depends on the type of noise and the intention of denoising.

You can find a wide range of research work in the field using a search machine.

**Remarks: **As you experience, it is difficult to filter out a massive noise from audio as soon as it is resident in the audio recording. In 2010 there were many attempts of Anti-Vuvuzela Filtering from different authors. I could not find a really satisfactory solution at that time.

A second observation is, that analog filtering is better than digital filtering in the example under consideration, because it works in real-time and you don’t get new additional noise by quantization errors. We tested a corresponding analog filter in an experiment in the physics practical course and the result confirmed this statement. Try and test it yourself.