An application of Fourier transform through Matlab in classifying tempos

Abstract

Mathematics is essential in life and its use can be seen in everything that involves numbers including in Digital Signal Processing (DSP). DSP is the process of analysing and modifying a signal so that its performance can be upgraded. This research is categorised under DSP because it involves the processing of audio music signals to obtain their respective tempos with the application of Fourier transform. Fourier transform is a mathematical algorithm that can break down a function into components of frequencies. The Fourier transform has the ability to convert time-domain signals of a music audio into frequency-domain signals and thus helps in producing the frequency spectrum needed to analyse the tempo of the music. In this research, Fourier transform was applied along with other signal processing functions such as filterbank, smoothing, windowing, differentiation and rectification to find the tempos of instrumental music excerpts from audio files in the .wav format. This research was developed to implement DSP with the aid of a Matlab program to obtain the tempos of music from a random selection of audio files involving several genres. In relation to this, it aimed to classify the audio files into slow and fast tempos to observe which audio music can promote relaxation (slow tempo) and whether it depends on the genre of music being listened to. This research was able to successfully process 40 audio files involving 5 music genres in the .wav format to obtain their respective tempos based on two parameters settings (60-150 BPM and 60-240 BPM) and classify them into two categories: the slow tempo (60 – 100 BPM) and fast tempo (> 100 BPM). By observation, it was found that all 5 genres contain at least one audio file with slow tempo which means that the relaxation state does not depend on the genre of music being listened to.