Coded data generation or conversion – Phase or time of phase change
Reexamination Certificate
2000-05-16
2002-12-31
Tokar, Michael (Department: 2819)
Coded data generation or conversion
Phase or time of phase change
C341S157000, C341S166000
Reexamination Certificate
active
06501399
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to audio signal processing and, more particularly, to a signal processor that produces an effect that resembles a live performance, restoring what was lost during the transduction and recording sequences.
2. Description of the Background
Some audio processing systems make use of amplitude or frequency adjustment or both, others rely on optimizing the Group Delays of frequencies; however, the current invention described herein converts audio information (changes in amplitude and frequency) into a phase space, where changes in amplitude and frequency become phase shifts of portions of a digital pulse. Regular loudspeakers can automatically decode the phase information, resulting in a virtually distortion-free analog acoustic signal whose bandwidth is approximately 0-50 KHz and whose characteristics include not only changes in amplitude and frequency, but, also, changes in phase as a function of frequency. It is obvious from the scientific literature that no coherent theory of hearing currently exists. Low frequency acoustic signals' wavelengths are much too large to enter the ear canal, and high frequencies (above 6 kHz) cause bifurcation of neuronal firing in the brain, allowing for subconscious processing of frequencies considered outside the (20-20 kHz) hearing range. The current invention expands the bandwidth of the audio signal from the “normal” frequency range to about 0-50 KHz, separates frequencies as a function of time, and converts ordinary stereo signals into phase distributed monaural. The result is a signal that interacts with the human brain in a new way to produce an effect that resembles a live performance, restoring what was lost during the transduction and recording sequences.
It was discovered in 1932 that hearing was not strictly physical, that psychological factors also contributed to our perception of sound (On Minimum Audible Sound Fields, by Sivian and White. Presented to the Acoustical Soc. of Am. at Ann Arbor, Mich. Nov. 29, 1932). That phase angles of even pure tones are sensed by humans was established in 1956 (Just Noticeable Differences in Dichotic Phase, by Zwislocki and Feldman, in J. Acous. Soc. of Am., Vol. 28, #5, September 1956). The ear is a non-linear device—current models and theories of hearing are based, primarily, on old, outdated linear models and concepts (Auditory Frequency Selectivity, edited by Moore and Patterson, NATO ASI series A, Vol 119, 1986). Some musical harmonics are non-linear (violin overtones, e.g.) (Regarding the Sound Quality of Violins and a Scientific Basis for Violin Construction, by H. Meinel, Ln, J. Acous. Soc. Am., Vol 29, #7, July 1957). The interaction of acoustic signals from various musical instruments (including Human voices and electronic synthesizers) create interference patterns that are embedded in the recording medium (tape, e.g.), but whose characteristics are ignored with current transducers and recording and playback equipment (Both Sides of the Mirror: Integrating Physics and Acoustics with Personal Experience, by Helen Hall, in, Leonardo Music Journal, vol 3, pp17-23, 1993). Just as laser processing of images focused on photographic emulsions can bring out the three-dimensional information in the two-dimensional image by retrieving phase information in the interference patterns, so this invention restores 3D information lost during transduction and recording. The result is a restoration of the “live” performance.
Classical theory indicates that acoustic events can be described in at least two ways; in a time domain or a frequency domain, each convertible into the other via a Fourier transformation. The mathematical formulation for this process is well known. The time-domain characterization of an acoustical event is a scalar, while the frequency-domain representation is a complex vector quantity containing amplitude and phase information. The time domain representation can also be expressed as a complex quantity. The scalar portion of the time domain vector represents performance based on impulse excitation; the imaginary part of the vector is the Hilbert transform of the scalar.
Loudspeakers and electrical networks which transfer energy from one form to another can be characterized by response to an impulse function, because the impulse response can be manipulated to predict the behavior of the system in response to any arbitrary signal. Fourier transforms work for predictive systems as well as causal systems. However, the group velocity of a set of audio signals is not related to time delay for all possible systems, and uniform group delay does not insurb a distortionless system. Group Delay is derived from phase delay, which is defined as the phase shift in a system at a given frequency. Group delay is associated with a group of frequencies around a central carrier, such as those encountered in modulated communications, but it also finds some relevance in describing how a system responds to a change in frequency. Group Delay follows an inverse square law. The value is fixed for DC but it approaches a finite value (near zero) at infinity. For a given function, and given the appropriate values for the resistor and capacitor, this logarithmic response will appear across the audio range. Starting with Tgd=2&agr;
0
/&agr;
0
2
+&ohgr;
2
, it can be shown that:
Tgd
(&ohgr;≈&agr;
0
)≈2.3/&agr;
0
log(&agr;
0
/&ohgr;)
For a simple case it is possible to relate a logarithmic approximation to the group delay. The approximation was developed around a region where alpha equals omega. A more general equation for a larger region is presented below. It was derived using similar techniques but spans the area from omega equals alpha to omega “large” (50K radians or so). Small values of omega are not permissible, and the error at omega equals alpha is significant. These logarithmic equations are not specifically necessary for the design process but when the user works with practical circuits, it will be noted (on test equipment) that the Group Delay of the audio bandwidth changes logarithmically with frequency. The following equation can be used to validate the observations; however, it is noted that because of the foregoing, Group Delay is rather meaningless and phase shift more accurately describes the true action of the circuit. Group Delay is included here to provide an alternate way of analyzing the circuit's action.
These two equations are generally equivalent for &ohgr;>5&agr;
0
:
Tgd
(&ohgr;)=2&agr;
0
/&agr;
0
2
+&ohgr;
2
Tgd
(&ohgr;)=2&agr;
0
*ln[1+(&agr;
0
/&ohgr;)]
2
The same equation rewritten for standard logarithms:
Tgd
(&ohgr;)=4.6/&agr;
0
*log[1+(&agr;
0
/&ohgr;)]
2
Interaural time difference, necessary for determining the position of a source, also has bearing on pitch. Further, most of the critical interaural time differences are in the range of plus or minus 1 millisecond. Thus, when the group delay is modified, so is the perception of the sound.
A generalized version of the All-pass response Group Delay is presented below. This equation can be used, with reasonable accuracy, to predict the group delay of a specific frequency for various RC combinations. It also accounts for Gain adjustments. Using these equations, one can tailor the Group Delay response. Referring to FIG.
5
:
&agr;
0
=1
/R
1
C
and
A=R
3
/R
2
.
The general transfer function is:
T
(
s
)=−
As−&agr;
0
/s+&agr;
0
which means the gain of the circuit is:
|
T
(
s
)|=−
A
The phase response is:
&phgr;(&ohgr;)=−2tan
−1
(&ohgr;
{square root over (A)}/&agr;
0
)
and the Group Delay is given by:
Tgd
(&ohgr;)=(
A+
1)&agr;
0
/&agr;
0
2
+&ohgr;
A
2
+A*
50 ns+100 ns
The second and third terms are included because their exclusion yields increasingly poor results with increasing frequencies. The above equations may be interpreted in the following physical sens
JeanGlaude Jean Bruner
Law Offices of Royal W. Craig
Tokar Michael
LandOfFree
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