Formant Analysis

Formants^[1] are the result of energy peaks in a more or less narrow zone of the spectrum. In short, they can be compared with resonances. More specifically, formants deal with vocal sounds : the reinforcement of several specific frequency zones in the spectrum of vocal sounds is perceived as vowels. Although the vocal apparatus has at least five resonators, three or four of them are considered to be crucial in the production of vowels :

• F1 : pharynx

• F2 : oral cavity

• F3 : nasal cavity (nasal vowels, in french for instance)

• F4 : sinuses (singing formant)

The formant analysis is accessed via the Analysis/Formant Analysis menu.

The spectral envelope is analysed to yield the frequencies of a number of formants, specified by the user.

A peak analysis is executed : depending on the parameters that were defined by the user, a number of resonators scan the spectral envelope.

The analysis is always applied to the whole sound file.

The spectral envelope can be calculated with two methods :

• LPC

• Discete Cepstrum

For detailed information about the LPC and discrete cepstrum, see the corresponding section.

Number of formants yielded in the SDIF file. By defaut, the 5 main formants are analysed.

A filter has

• a central frequency

• a bandwidth

• a stopband with an attenuation rate, or slope.

The analysis order represents the filter – or resonator – complexity. If our filter was a physical filter, this would represent the number of inductors and capacitors, which emphasize or filter the spectral components.

The filter's response is optimal with little energy for a given frequency, within a given passband. Once the limit of the passband is reached, its response decreases more or less progressively for neighbour partials : this characterizes the slope.

The slope's steefness depends on the filter's complexity. The more complex the filter, the steefest is the slope of the passband : the higher the attenuation rate is, as the frequency decreases.

This rate can be calculated as follows. For n poles, we have

• –6n dB/octave 

• –20n dB/decade

An octave is a doubling or halving of the frequency; a decade is a tenfold increase or decrease of frequency.

An LPC analysis requires at least two poles per formant.

We have analysed a short extract of a Rilke's poem. The LPC shows the various zones of energy reinforcement in the spectrum. Especially, some zones show important transitions between two vowels (at the end a closed and an open e/ɛ for instance).

We want to get the 5 first formants of the spectrum. We have tried several number of poles, from 20 to 60. If we convert the SDIF file into a text file with SDIF Converter, considering only the time, frequency and amplitude, the values for each formant will be displayed one after the other for a given point in time.

Here is an example of the data we get with 60 poles at three different locations of the file :

The values match a visual estimation of the formants quite precisely. They are quite close to those of a tenor voice, but this is only an indication. Note that the first formant of the e and the second formant of the i are missing.