Signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniq ...
is an
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
subfield that focuses on analysing, modifying, and synthesizing
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
s such as
sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
,
images
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
, and scientific measurements.
For example, with a
filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
''g'', an inverse filter ''h'' is one such that the sequence of applying ''g'' then ''h'' to a signal results in the original signal. Software or electronic inverse filters are often used to compensate for the effect of unwanted environmental filtering of signals.
In speech science
In all proposed models for the production of
human speech
Speech is a human vocal communication using language. Each language uses phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound different from all French words, even if they are th ...
, an important variable is the waveform of the airflow, or volume velocity, at the
glottis
The glottis is the opening between the vocal folds (the rima glottidis). The glottis is crucial in producing vowels and voiced consonants.
Etymology
From Ancient Greek ''γλωττίς'' (glōttís), derived from ''γλῶττα'' (glôtta), va ...
. 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
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
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
[M. Rothenberg, ''A new inverse-filtering technique for deriving the glottal air flow waveform during voicing'', J. Acoust. Soc. Amer., Vol. 53, #6, 1632 - 1645](_blank)
/ref> 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
Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in Ce ...
, more commonly referred to as resonances or formant
In speech science and phonetics, a formant is the broad spectral maximum that results from an acoustic resonance of the human vocal tract. In acoustics, a formant is usually defined as a broad peak, or local maximum, in the spectrum. For harmoni ...
s. Thus, an inverse-filter would have a pair of complex-conjugate zeroes, more commonly referred to as an anti-resonance In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of an oscillator at a particular frequency, accompanied by a large, abrupt shift in its oscillation phase. Such frequencies ...
, for every vocal tract formant in the frequency range of interest.
If the input is from a microphone
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
, 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
In systems theory, 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 nonlinear case.
As a mathematical abstraction o ...
, however, the source and filter need not be independent.
References
{{Speech synthesis
Speech synthesis