Juhan Nam

Alias-Suppressed Oscillators Based on Differentiated Polynomial Waveforms

An efficient approach to the generation of classical synthesizer waveforms with reduced aliasing is proposed. This paper introduces two new classes of polynomial waveforms that can be differentiated one or more times to obtain an improved version of the sampled sawtooth and triangular signals. The differentiated polynomial waveforms (DPW) extend the previous differentiated parabolic wave method to higher polynomial orders, providing improved alias-suppression. Suitable polynomials of order higher than two can be derived either by analytically integrating a previous lower order polynomial or by solving the polynomial coefficients directly from a set of equations based on constraints. We also show how rectangular waveforms can be easily produced by differentiating a triangular signal. Bandlimited impulse trains can be obtained by differentiating the sawtooth or the rectangular signal. An objective evaluation using masking and hearing threshold models shows that a fourth-order DPW method is perceptually alias-free over the whole register of the grand piano. The proposed methods are applicable in digital implementations of subtractive sound synthesis.

Efficient Antialiasing Oscillator Algorithms Using Low-Order Fractional Delay Filters

One of the challenges in virtual analog synthesis is avoiding aliasing when generating classic waveforms such as sawtooth and square wave which have theoretically infinite bandwidth in their ideal forms. The human auditory system renders a certain amount of aliasing inaudible, which allows room for finding cost-effective algorithms. This paper suggests efficient algorithms to reduce the aliasing using low-order fractional delay filters in the framework of bandlimited impulse train (BLIT) synthesis. Examining Lagrange, B-spline interpolators and allpass fractional delay filters, optimized methods will be discussed for generating classic waveforms (sawtooth, square, and triangle). Techniques for generating more complicated harmonics such as pulse width modulation, hard-sync, and super-saw are also presented. The perceptual evaluation is performed by comparing the threshold of hearing and masking curve of oscillators with their aliasing levels. The result shows that the BLIT using the computationally efficient third-order B-spline generates waveforms that are perceptually free of aliasing within practically used fundamental frequencies.

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz.

Acoustic scene classification using sparse feature learning and event-based pooling

Recently unsupervised learning algorithms have been successfully used to represent data in many of machine recognition tasks. In particular, sparse feature learning algorithms have shown that they can not only discover meaningful structures from raw data but also outperform many hand-engineered features. In this paper, we apply the sparse feature learning approach to acoustic scene classification. We use a sparse restricted Boltzmann machine to capture manyfold local acoustic structures from audio data and represent the data in a high-dimensional sparse feature space given the learned structures. For scene classification, we summarize the local features by pooling over audio scene data. While the feature pooling is typically performed over uniformly divided segments, we suggest a new pooling method, which first detects audio events and then performs pooling only over detected events, considering the irregular occurrence of audio events in acoustic scene data. We evaluate the learned features on the IEEE AASP Challenge development set, comparing them with a baseline model using mel-frequency cepstral coefficients (MFCCs). The results show that learned features outperform MFCCs, event-based pooling achieves higher accuracy than uniform pooling and, furthermore, a combination of the two methods performs even better than either one used alone.

Sound recognition in mixtures

In this paper, we describe a method for recognizing sound sources in a mixture. While many audio-based content analysis methods focus on detecting or classifying target sounds in a discriminative manner, we approach this as a regression problem, in which we estimate the relative proportions of sound sources in the given mixture. Using source separation ideas based on probabilistic latent component analysis, we directly estimate these proportions from the mixture without actually separating the sources. We also introduce a method for learning a transition matrix to temporally constrain the problem. We demonstrate the proposed method on a mixture of five classes of sounds and show that it is quite effective in correctly estimating the relative proportions of the sounds in the mixture.

Optimized Polynomial Spline Basis Function Design for Quasi-Bandlimited Classical Waveform Synthesis

Classical geometric waveforms used in virtual analog synthesis suffer from aliasing distortion when simple sampling is used. An efficient antialiasing technique is based on expressing the waveforms as a filtered sum of time-shifted approximately bandlimited polynomial-spline basis functions. It is shown that by optimizing the coefficients of the basis function so that the aliasing distortion is perceptually minimized, the alias-free bandwidth of classical waveforms can be expanded. With the best of the case examples given here, the generated impulse-train and sawtooth waveform are alias-free up to fundamental frequencies over 10 kHz when the sampling rate is 44.1 kHz.

Variable fractional delay filters in bandlimited oscillator algorithms for music synthesis

Trivially sampled geometric waveforms such as the rectangular pulse wave used in subtractive sound synthesis suffer from aliasing caused by the discontinuities in the waveform or its derivative. Several algorithms for the reduction of aliasing distortion have been suggested, providing either complete removal or great suppression of aliasing. Some antialiasing oscillators utilize variable fractional delay filters as an essential part of the algorithm. In this paper, these oscillators are reviewed with an emphasis on motivating the use of the fractional delay filters.