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this paper the interest is in separating these two elements of the sound and finding parametric representations with musical meaning. To do so a local harmonic model that tracks changes in pitch and in the amplitudes of the harmonics is fit. Deterministic changes in the signal, such as pitch change, suggest that different temporal window sizes should be considered. Ways to choose appropriate window sizes are studied. Amongst other things our analysis provides estimates of the harmonic signal and of the noise signal. Different musical composition applications may be based on the estimates. KEY WORDS: Musical Sound Signals, Local Harmonic Model, Widow Size Selection 1. INTRODUCTION Statistics has been applied in various ways to music. For example, various stochastic techniques have been applied in composition (Jones 1981). Stochastic techniques have also been used in forecasting unfinished works (Dirst and Weigend 1992). Voss and Clarke (1975) studied the spectral properties of different musical signals and speculated on the possibility of it being so called 1/f noise. In Brillinger and Irizarry (1998) this is studied in more detail, and in particular higher order statistics are examined. In this paper the particular application that will be examined in detail is the analysis of sound signals produced by musical instruments. In this field, statistical techniques have been used, for example, to separate the signals into what are believed to be deterministic and stochastic parts and to deconstruct the deterministic part into harmonic components.

Modern speech processing applications require operation on signal of interest that is contaminated by high level of noise. This situation calls for a greater robustness in estimation of the speech parameters, a task which is hard to achieve using standard speech models. In this paper, we present an optimal estimation procedure for sound signals (such as speech) that are modeled by harmonic sources. The harmonic model achieves more robust and accurate estimation of voiced speech parameters. Using maximum a posteriori probability framework, successful tracking of pitch parameters is possible in ultra low signal to noise conditions (as low as 15 dB). The performance of the method is evaluated using the Keele pitch detection database with realistic background noise. The results show best performance in comparison to other state-of-the-art pitch detectors. Application of the proposed algorithm in a simple speaker identification system shows significant improvement in the performance.

This report centres around some of this issues involved in automatic transcription of polyphonic musical audio signals. That is, representing the information contained in the audio in such a way as to be recognisable and usable by a musician. First, a review of the various fields which have a bearing on the subject is put forward, including music, music psychology, auditory psychology and signal processing. Then a thorough appraisal of previous work on automated polyphonic transcription is presented. Next, original work on the use of time-frequency reassignment as a front end is imparted and finally, future ideas are expounded and a timetable for forthcoming research is given.

After a survey of inverse transform methods for the efficient synthesis of narrow-band and broad-band signals, a novel spectral line broadening technique is introduced for synthesis of pitch modulated noise signals. This new transform-domain approach is compared to the time-domain oscillator method with respect to their relative efficiency on modern processors Introduction: Noise in Musical Instrument Sounds The term "noise" is used to describe the perception of a multitude of features of sounds from musical instruments, for example: . Dense modes, e.g., cymbals . Additive "noise" from turbulence in blown instruments such as the flute or consonants in the voice. . Impulses from short-term interactions such as hammer strikes, string plucks, key and tone hole closure and openings. . Bandwidth broadening from non-linear mechanisms such as piano dampers, harpsichord quills, tampoura and the sarod jawari bridge. . Correlated or convolutional noise in blown instruments where a reed (o...

The study of musical sound has become a popular research field. Harmonic regression signal plus noise statistical models have been used to analyze sound signals. However, it is common to give estimates of harmonic parameters without indications of their uncertainties. Least squares estimates for harmonic models have been studied and asymptotic variance expression have been developed. In practice, window based estimates are used. This paper studies the statistical properties of such estimates, in particular we use asymptotic variance expressions to develop standard errors and construct confidence intervals. We present applications and examples of the statistical techniques to musical sound signal analysis.

: Window-based estimates for stochastic harmonic regression models are useful for cases where harmonic parameters appear to be time-varying. Least squares estimates for harmonic models with one fundamental have been studied and asymptotic variance expressions have been developed. This paper extends these results to weighted least squares for the multiple fundamental case, and presents an application in signal processing. Key words and phrases: Asymptotic variance, harmonic regression, signal processing, sound analysis, time-varying parameters, weighted least squares estimates. 1. Introduction Consider the signal plus noise model y t = s(t; fi) + ffl t ; (t = 1; : : : ; T ); (1) where the signal s(t; fi) is composed of J periodic components s(t; fi) = J X j=1 s j (t; fi j ); fi = (fi 1 ; : : : ; fi J ) 0 (2) and each component s j (t; fi j ) is a sum of K j sinusoidal components s j (t; fi j ) = K j X k=1 fA j;k cos(! j;k t) +B j;k sin(! j;k t)g (3) fi j = (A j;1 ; B j;1 ;...