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, Scalar potential, potential fields, Seismic tomograph ...

is an

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

subfield that focuses on analysing, modifying, and synthesizing

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

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 br ...

images An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a project ...

, and scientific measurements. For example, with a filter ''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, an important variable is the waveform of the airflow, or volume velocity, at the

glottis The glottis (: glottises or glottides) is the opening between the vocal folds (the rima glottidis). The glottis is crucial in producing sound from the vocal folds. Etymology From Ancient Greek ''γλωττίς'' (glōttís), derived from ''γ ...

. 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 publi ...

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 RothenbergM. Rothenberg, ''A new inverse-filtering technique for deriving the glottal air flow waveform during voicing'', J. Acoust. Soc. Amer., Vol. 53, #6, 1632 - 1645
/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 Pole or poles may refer to: People *Poles (people), another term for Polish people, from the country of Poland * Pole (surname), including a list of people with the name * Pole (musician) (Stefan Betke, born 1967), German electronic music artist ...

, 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 harmo ...

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

, 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 abstractio ...

, however, the source and filter need not be independent.

References

{{Speech synthesis Speech synthesis