Inverse filter
Encyclopedia
In all proposed models for the production of human speech, an important variable is the waveform of the airflow, or volume velocity, at the glottis
. The glottal volume velocity waveform provides the link between movements of the vocal folds and the acoustical results of such movements, in that the glottis acts approximately as a source of volume velocity. That is, the impedance of the glottis is usually much higher than that of the vocal tract, and so glottal airflow is controlled mostly (but not entirely) by glottal area and subglottal pressure, and not by vocal-tract acoustics. This view of voiced speech production is often referred to as the source-filter model
.
A technique for obtaining an estimate of the glottal volume velocity waveform during voiced speech is the “inverse-filtering” of either the radiated acoustic waveform, as measured by a microphone
having a good low frequency response, or the volume velocity at the mouth, as measured by a pneumotachograph at the mouth having a linear response, little speech distortion, and a response time of under approximately 1/2 ms. A pneumotachograph having these properties was first described by Rothenberg and termed by him a circumferentially vented mask or CV mask.
As practiced, inverse-filtering is usually limited to non-nasalized or slightly nasalized vowels, and the recorded waveform is passed through an “inverse-filter” having a transfer characteristic that is the inverse of the transfer characteristic of the supraglottal vocal tract configuration at that moment. The transfer characteristic of the supraglottal vocal tract is defined with the input to the vocal tract considered to be the volume velocity at the glottis. For non-nasalized vowels, assuming a high-impedance volume velocity source at the glottis, the transfer function of the vocal tract below about 3000 Hz contains a number of pairs of complex-conjugate poles, more commonly referred to as resonances or formant
s. Thus, an inverse-filter would have a pair of complex-conjugate zeroes
, more commonly referred to as an anti-resonance, for every vocal tract formant in the frequency range of interest.
If the input is from a microphone
, and not a CV mask or its equivalent, the inverse filter also must have a pole at zero frequency (an integration operation) to account for the radiation characteristic that connects volume velocity with acoustic pressure. Inverse filtering the output of a CV mask retains the level of zero flow, while inverse filtering a microphone signal does not.
Inverse filtering depends on the source-filter model and a vocal tract filter that is linear system
, however, the source and filter need not be independent.
Glottis
The glottis is defined as the combination of the vocal folds and the space in between the folds .-Function:...
. The glottal volume velocity waveform provides the link between movements of the vocal folds and the acoustical results of such movements, in that the glottis acts approximately as a source of volume velocity. That is, the impedance of the glottis is usually much higher than that of the vocal tract, and so glottal airflow is controlled mostly (but not entirely) by glottal area and subglottal pressure, and not by vocal-tract acoustics. This view of voiced speech production is often referred to as the source-filter model
Source-filter model of speech production
The source–filter model of speech production models speech as a combination of a sound source, such as the vocal cords, and a linear acoustic filter, the vocal tract . An important assumption that is often made in the use of the source-filter model is the independence of source and filter...
.
A technique for obtaining an estimate of the glottal volume velocity waveform during voiced speech is the “inverse-filtering” of either the radiated acoustic waveform, as measured by a microphone
Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...
having a good low frequency response, or the volume velocity at the mouth, as measured by a pneumotachograph at the mouth having a linear response, little speech distortion, and a response time of under approximately 1/2 ms. A pneumotachograph having these properties was first described by Rothenberg and termed by him a circumferentially vented mask or CV mask.
As practiced, inverse-filtering is usually limited to non-nasalized or slightly nasalized vowels, and the recorded waveform is passed through an “inverse-filter” having a transfer characteristic that is the inverse of the transfer characteristic of the supraglottal vocal tract configuration at that moment. The transfer characteristic of the supraglottal vocal tract is defined with the input to the vocal tract considered to be the volume velocity at the glottis. For non-nasalized vowels, assuming a high-impedance volume velocity source at the glottis, the transfer function of the vocal tract below about 3000 Hz contains a number of pairs of complex-conjugate poles, more commonly referred to as resonances or formant
Formant
Formants are defined by Gunnar Fant as 'the spectral peaks of the sound spectrum |P|' of the voice. In speech science and phonetics, formant is also used to mean an acoustic resonance of the human vocal tract...
s. Thus, an inverse-filter would have a pair of complex-conjugate zeroes
Zero (complex analysis)
In complex analysis, a zero of a holomorphic function f is a complex number a such that f = 0.-Multiplicity of a zero:A complex number a is a simple zero of f, or a zero of multiplicity 1 of f, if f can be written asf=g\,where g is a holomorphic function g such that g is not zero.Generally, the...
, more commonly referred to as an anti-resonance, for every vocal tract formant in the frequency range of interest.
If the input is from a microphone
Microphone
A microphone is an acoustic-to-electric transducer or sensor that converts sound into an electrical signal. In 1877, Emile Berliner invented the first microphone used as a telephone voice transmitter...
, and not a CV mask or its equivalent, the inverse filter also must have a pole at zero frequency (an integration operation) to account for the radiation characteristic that connects volume velocity with acoustic pressure. Inverse filtering the output of a CV mask retains the level of zero flow, while inverse filtering a microphone signal does not.
Inverse filtering depends on the source-filter model and a vocal tract filter that is linear system
Linear system
A linear system is a mathematical model of a system based on the use of a linear operator.Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case....
, however, the source and filter need not be independent.