Aliasing reduction in clipped signals

Most real-world audio devices, particularly those of interest in musical applications, fall under the category of nonlinear systems. Examples of these devices include overdrive and distortion circuits used by guitar and bass players, dynamic range processors, and vintage synthesizer circuits. Nonlinear algorithms are known to expand the bandwidth of the input signal by introducing harmonic and intermodulation distortion. Naive digital emulations of these systems are susceptible to aliasing due to the inherent frequency constraints of discrete systems.  This thesis focuses on new digital signal processing techniques designed to reduce the level of aliasing introduced by memoryless nonlinearities. The underlying motivation of this work is to incorporate these tools within the framework of virtual analog (VA) modeling, an area of study that concentrates on the emulation of analog audio devices in the digital domain. In VA modeling, aliasing reduction has been studied extensive for the case of synthesis of classical oscillator waveforms like those used in subtractive synthesis. However, in audio effects processing oversampling has traditionally been the only available tool to ameliorate this problem. The first part of this work proposes the use of bandlimited correction functions previously used in waveform synthesis, to reduce the aliasing caused by special nonlinearities that introduce discontinuities in the derivatives of a signal. This family of novel methods includes the use of the bandlimited ramp function (BLAMP), its efficient polynomial approximations, and its integrated form. A new VA model of a highly nonlinear wavefolder circuit, which incorporates one of these techniques, is proposed.  The second family of techniques elaborated in this thesis is that of the antiderivative method. This innovative approach to aliasing reduction is based on the discrete differentiation of integrated nonlinearities and can be applied to arbitrary explicit memoryless nonlinearities regardless of their form. The use of the antiderivative forms in VA modeling is proposed by introducing two novel transistor/diode-based wavefolder models, and two static diode clipper models that incorporate these techniques.  Results obtained show the proposed algorithms effectively reduce the level of aliasing in nonlinear processing and can help reduce, and in some cases even eliminate, the oversampling requirements of the system. The proposed algorithms are suitable for real-time software implementations of VA instruments and effects processors

On Unlimited Sampling

Shannon's sampling theorem provides a link between the continuous and the discrete realms stating that bandlimited signals are uniquely determined by its values on a discrete set. This theorem is realized in practice using so called analog--to--digital converters (ADCs). Unlike Shannon's sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some preset threshold, the ADC saturates, resulting in aliasing due to clipping. The goal of this paper is to analyze an alternative approach that does not suffer from these problems. Our work is based on recent developments in ADC design, which allow for ADCs that reset rather than to saturate, thus producing modulo samples. An open problem that remains is: Given such modulo samples of a bandlimited function as well as the dynamic range of the ADC, how can the original signal be recovered and what are the sufficient conditions that guarantee perfect recovery? In this paper, we prove such sufficiency conditions and complement them with a stable recovery algorithm. Our results are not limited to certain amplitude ranges, in fact even the same circuit architecture allows for the recovery of arbitrary large amplitudes as long as some estimate of the signal norm is available when recovering. Numerical experiments that corroborate our theory indeed show that it is possible to perfectly recover function that takes values that are orders of magnitude higher than the ADC's threshold.Comment: 11 pages, 4 figures, copy of initial version to appear in Proceedings of 12th International Conference on Sampling Theory and Applications (SampTA

The sensitivity of a very long baseline interferometer

The theoretical sensitivity of various methods of acquiring and processing interferometer data are compared. It is shown that for a fixed digital recording capacity one bit quantization of single sideband data filtered with a rectangular bandpass and sampled at the Nyquist rate yields the optimum signal to noise ratio. The losses which result from imperfect bandpass, poor image rejection, approximate methods of fringe rotation, fractional bit correction, and loss of quadrature are discussed. Also discussed is the use of the complex delay function as a maximum likelihood fringe estimator

Integrating a Non-Uniformly Sampled Software Retina with a Deep CNN Model

We present a biologically inspired method for pre-processing images applied to CNNs that reduces their memory requirements while increasing their invariance to scale and rotation changes. Our method is based on the mammalian retino-cortical transform: a mapping between a pseudo-randomly tessellated retina model (used to sample an input image) and a CNN. The aim of this first pilot study is to demonstrate a functional retinaintegrated CNN implementation and this produced the following results: a network using the full retino-cortical transform yielded an F1 score of 0.80 on a test set during a 4-way classification task, while an identical network not using the proposed method yielded an F1 score of 0.86 on the same task. The method reduced the visual data by e×7, the input data to the CNN by 40% and the number of CNN training epochs by 64%. These results demonstrate the viability of our method and hint at the potential of exploiting functional traits of natural vision systems in CNNs

Properties of M31. II: A Cepheid disk sample derived from the first year of PS1 PAndromeda data

We present a sample of Cepheid variable stars towards M31 based on the first year of regular M31 observations of the PS1 survey in the r_P1 and i_P1 filters. We describe the selection procedure for Cepheid variable stars from the overall variable source sample and develop an automatic classification scheme using Fourier decomposition and the location of the instability strip. We find 1440 fundamental mode (classical \delta) Cep stars, 126 Cepheids in the first overtone mode, and 147 belonging to the Population II types. 296 Cepheids could not be assigned to one of these classes and 354 Cepheids were found in other surveys. These 2009 Cepheids constitute the largest Cepheid sample in M31 known so far and the full catalog is presented in this paper. We briefly describe the properties of our sample in its spatial distribution throughout the M31 galaxy, in its age properties, and we derive an apparent period-luminosity relation (PLR) in our two bands. The Population I Cepheids nicely follow the dust pattern of the M31 disk, whereas the 147 Type II Cepheids are distributed throughout the halo of M31. We outline the time evolution of the star formation in the major ring found previously and find an age gradient. A comparison of our PLR to previous results indicates a curvature term in the PLR