Computer Science Project



Frequency analysis

The sounds produced by a sound source are normally not just one frequency as in the diapason of figure 1. Are not pure, but consist of several frequencies simultaneously. A piano, for example, produce sounds with frequencies between 27.5 Hz and 4186 Hz, the human ear, can detect frequencies in the range between 20 Hz and 20.000 Hz. Below 20 Hz, the sounds (inaudible) designate infrasonic sounds and above 20000Hz (again inaudible) are called ultrasonic.

Fig.1 Diapason vibration

A French mathematician, Jean Baptiste Joseph Fourier (1768-1830), demonstrated that any form of wave is the sum of many sinusoids with different characteristics. For example, each instrument has a sound typical, called Timbre [property of sound that distinguishes sounds with the same intensity and different frequency (height), but from different sound sources. The note C of a piano is not the same C as a violin or a flute], and can be decomposed into a sum of several sinusoids. This decomposition is called the Spectrum of Sound, and is done through the FFT (Fast Fourier Transform).

A microphone placed in a sound field can determine the changes in pressure. If we have a graph of the sound pressure level(dB), in order y-axis, and the corresponding frequency in x-axis, we obtain what is called the spectrum or sound spectrum in frequency of a sound. For example, three separate diapasons create a discrete spectrum, such as that shown in figure 2. Any sound source or a noise , in general, give a spectrum with a multitude of components.


Fig.3 Spectrum of three diapasons

Noise frequency analysis

If we wanted  measure the acoustic spectrum of a sound source in all its audible range was almost certainly impossible. In order to measure only the part that interests us, we would have to pass the electrical signal produced by a band-pass filter very narrow (Figure 4), thus removing all other frequencies, and calculate its value RMS.

Fig.4 Band-pass filter


Even using a filter with a width of 1 Hz would have required 19980 filters (one for each frequency that is heard by the human ear, 20Hz to 20000Hz) in order to obtain the desired spectrum. Such analysis, in addition to extremely lengthy, will be very expensive. So are used filters, not to isolate individual frequencies, but to isolate ranges or frequency bands. One of the most widely used is the octave filters, where the highest frequency leaky double the frequency is lower (Figure 5).

Fig.5  Octave filter

In the project I have used “Spectro” (Software from NVHsoftware) to analyse the frequencies that are present in the collected noise. First I have record the sound from the frequencies: 100Hz, 250Hz, 500Hz, 1000Hz and 2000Hz with a sound generator “AudioWave” (Software from ABACOM).  By comparison between  the  charts of the two  programs we can see  the predominant frequencies.

Figures 6 / 7 show the 500 Hz frequency, figures 8 /9 show the 1000Hz frequency and 10 /11 the street noise. If we click in the Windows Media Player figures we can hear the sound.


Fig.6   500Hz sound


Fig.7   500Hz analysed





Fig.8   1000Hz sound


Fig.9   1000Hz analysed

Fig.10   Street sound

Fig.11   Street sound analysed



We can see in figure 11 the set of frequencies related with the street noise at 6 pm. The frequencies around 1000Hz are predominant and the intensity is around 60 to 70dB(A).

This type of analysis is very important because if we know the frequencies of the noise, perhaps we can found better ways to control the problem of the noise pollution.




JM Freixo Nunes © 2009