Final Written Review - High and Low Shelf Tone Shaper

The characteristics of analogue audio processors are useful and valued for musical applications. A function has been implemented that allows the user to easily and intuitively introduce and control non linear behaviours and produce an output signal that has some of the characteristics that are valued in the analogue processing domain

Antiderivative antialiasing for memoryless nonlinearities

Aliasing is a commonly encountered problem in audio signal processing, particularly when memoryless nonlinearities are simulated in discrete time. A conventional remedy is to operate at an oversampled rate. A new aliasing reduction method is proposed here for discrete-time memoryless nonlinearities, which is suitable for operation at reduced oversampling rates. The method employs higher order antiderivatives of the nonlinear function used. The first-order form of the new method is equivalent to a technique proposed recently by Parker et al. Higher order extensions offer considerable improvement over the first antiderivative method, in terms of the signal-to-noise ratio. The proposed methods can be implemented with fewer operations than oversampling and are applicable to discrete-time modeling of a wide range of nonlinear analog systems.Peer reviewe

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