Music – Instruments – Electrical musical tone generation
Reexamination Certificate
1997-12-12
2001-07-10
Witkowski, Stanley J. (Department: 2837)
Music
Instruments
Electrical musical tone generation
C084S660000, C084S661000, C084SDIG009
Reexamination Certificate
active
06259014
ABSTRACT:
This invention relates generally to methods for musical signal analysis and synthesis and, in particular, to analysis and synthesis of musical tones or notes using sinusoidal modeling.
BACKGROUND OF THE INVENTION
A generic analysis-based music synthesis system is depicted in FIG.
1
. In the analysis part, a parametric representation of a music record is estimated using a musical sound model. In the synthesis part, the parametric representation or its transformation is used to produce a synthesized record.
The idea of creating musical sounds using sinusoidal models is at least a century old. See, C. Roads,
The Computer Music Tutorial
(1996 MIT Press) p.134, for a brief survey. The first music synthesizer
Talharmonium
produced complex tones by mixing sine wave harmonics from dozens of electrical tone generators. See, U.S. Pat. Nos. 580,035; 1,107,261; 1,213,803; and 1,295,691. The sinusoidal model is also the model used in most contemporary analysis-based music synthesis techniques, including pitch-synchronous analysis (J. C. Risset, et al., “Analysis of Musical Instrument Tones,”
Physics Today, vol.
22, no. 2, pp. 23-40 (1969)), synthesis heterodyne filter technique (J A Moorer, “
On the Segmentation and Analysis of Continuous Musical Sound By Digital Computer
,” PhD Thesis, Stanford University (1975)), the phase vocoder (J. L. Flanagan et al., “Phase Vocoder,”
Bell System Tech. Journal
(November 1966) and M. Dolson, “The Phase Vocoder: A Tutorial,”
Computer Music Journal,
vol. 10, no. 4 (1986)), sinusoidal transformation system (STS) (R. J. McAulay et al., “Speech Analysis/Synthesis Based on a Sinusoidal Representation,”
IEEE Trans. On Acoustics, Speech and Signal Processing,
vol. 34, pp. 744-754 (August 1986)), spectral modeling system (SMS) (X. Serra et al., “Spectral Modeling System: A Sound Analysis/Synthesis System Based on a Deterministic Plus Stochastic Decomposition,”
Computer Music Journal,
vol. 14, no. 4 (1990), and ABS/OLA (E. B. George et al., “Analysis-by-Synthesis/Overlap-Add Sinusoidal Modeling Applied to the Analysis and Synthesis of Musical Tones,”
Journal of Audio Engineering Society,
vol. 40, no. 6, pp. 497-516 (1992)).
Despite the power of the sinusoidal model, modeling the music signal exclusively with sinusoids can lead to an “information explosion” due to the large number of sinusoidal components needed for modeling the “noisy” component in the original sound or/and the many harmonics in the low-pitched musical sounds. The large volume of analyzed parameters can be cumbersome for musicians to manipulate and can also cause difficulties and/or high cost for storage in a synthesizer.
Two approaches have been used to reduce the number of model parameters. One approach is described in J. M. Grey, “
An Exploration of Musical Timbre
,” PhD Thesis, Stanford University (1975) and the R. J. McAulay et al. article, referenced above. That approach estimates the model parameters (such as amplitude and frequency) only at certain “break” points (frame boundaries) rather than at every sample point. The parameters are subsequently interpolated to all sample points at the synthesis stage. The other approach is described in the X. Serra et al. article, referenced above. That approach models the “noisy” part of the original sound other than with sine wave clusters. The latter approach is advantageous because it not only makes the signal model more parsimonious, thus removing some of the artificial tonal quality sometimes perceived in the synthesized sound when the noisy component is modeled by orderly sine wave clusters, but it also makes the signal model more accurate. This invention builds on both approaches.
SUMMARY OF THE INVENTION
The invention provides novel methods for musical signal analysis and synthesis. The assumption is made that musical tones can be adequately modeled by the sum of a sinusoidal part and a non-sinusoidal part, as shown by equation (1) below. The non-sinusoidal part may be referred to as the stochastic part or “residual” of the analyzed signal.
s
(
t
)
=
∑
m
=
1
M
A
m
(
t
)
sin
(
ω
m
t
+
θ
m
(
t
)
)
+
e
(
t
)
.
(
1
)
In equation (1), the sinusoidal part is specified by amplitude tracks A
m
(t), nominal frequencies &ohgr;
m
and phase deviation tracks &thgr;
m
(t) (1≦m≦M). The residual, or stochastic part, is denoted by e(t). The invention provides mechanisms for estimating the model parameters and for developing a corresponding synthesis procedure to reconstruct the original tones or to transform and modify them to achieve desired musical effects.
Experiments have shown that different physical bases exist for generation of the sinusoidal and stochastic parts. The physics of some musical instruments requires that the sinusoidal and stochastic parts be handled separately and differently.
The invention provides ways to estimate the sinusoidal parameters and model the stochastic part. For the sinusoidal part, the model parameters are estimated by minimizing the error between the analyzed and the reconstructed signal waveforms in a least square sense. The minimization procedure is conducted over the entire signal duration. This is in contrast to the (short-time) Fourier transform based methods of McAulay et al., Serra et al. and George et al., above, where parameters are estimated on a frame-by-frame basis in order to account for the time-varying nature of the signal being analyzed. For this reason, the proposed analysis approach is referred to as a global waveform fitting (GWF method).
The advantages of GWF are its analysis accuracy and the resulting synthesis efficiency and quality. The analysis accuracy of the sinusoidal parameters is enhanced in GWF by removing two limitations of the frame-based Fourier methods: One limitation is that the parameters are estimated using only the signal waveform in the local data frame without “looking-ahead” or “looking-back.” Another limitation is the well-known window effect caused by truncating the signal waveform. In GWF, the constraints imposed by the whole signal waveform on the local parameters are exploited and, therefore, the estimation resolution is not limited by the frame length. Another advantage of GWF is that it takes essentially an analysis-by-synthesis approach, and thus the synthesized waveform directly fits to the original waveform. This is contrary to the approach taken in Serra et al. and McAulay et al. wherein the model parameters are first estimated at frame boundaries and then the synthesized waveform is constructed from interpolated parameters.
The main benefits of GWF at the synthesis stage are the reduction of storage requirement and increase in computational efficiency. GWF reduces the parameters from three per frame to two per frame and eliminates one of the three additions to compute a phase sample. It is hoped that this reduction in resource requirement and the receding cost of high speed digital signal processors will finally bring the analysis-based additive synthesizer to reality. The increased accuracy of waveform fitting also translates into high fidelity of the synthesized sound.
REFERENCES:
patent: 3992971 (1976-11-01), Chibana et al.
patent: 4135422 (1979-01-01), Chibana
patent: 4142432 (1979-03-01), Kameyama et al.
patent: 4961364 (1990-10-01), Tsutsumi et al.
patent: 5665928 (1997-09-01), Wang
Ding Yinong
Qian Xiaoshu
Brady W. James
Hoel Carlton H.
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
Witkowski Stanley J.
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