Download Robust Design of Very High-Order Allpass Dispersion Filters
A nonparametric allpass filter design method is presented for matching a desired group delay as a function of frequency. The technique is useful in physical modeling synthesis of musical instruments and emulation of audio effects devices exhibiting dispersive wave propagation. While current group delay filter design methods suffer from numerical difficulties except at low filter orders, the technique presented here is numerically robust, producing an allpass filter in cascaded biquad form, and with the filter poles following a smooth loop within the unit circle. The technique was inspired by the observation that a pole-zero pair arranged in allpass form contributes exactly 2π radians to the integral of group delay around the unit circle, regardless of the (stable) pole location. To match a given group delay characteristic, the method divides the frequency axis into sections containing 2π total area under the desired group-delay curve, and assigns a polezero allpass pair to each. In this way, the method incorporates an order selection technique, and by adding a pure delay to the desired group delay, allows the trading of increased filter order for improved fit to the frequency-dependent group delay. Design examples are given for modeling the group delay of a dispersive string (such as a piano string), and a dispersive spring, such as in a spring reverberator.
Download Simplified, Physically-Informed Models of Distortion and Overdrive Guitar Effects Pedals
This paper explores a computationally efficient, physically informed approach to design algorithms for emulating guitar distortion circuits. Two iconic effects pedals are studied: the “Distortion” pedal and the “Tube Screamer” or “Overdrive” pedal. The primary distortion mechanism in both pedals is a diode clipper with an embedded low-pass filter, and is shown to follow a nonlinear ordinary differential equation whose solution is computationally expensive for real-time use. In the proposed method, a simplified model, comprising the cascade of a conditioning filter, memoryless nonlinearity and equalization filter, is chosen for its computationally efficient, numerically robust properties. Often, the design of distortion algorithms involves tuning the parameters of this filter-distortion-filter model by ear to match the sound of a prototype circuit. Here, the filter transfer functions and memoryless nonlinearities are derived by analysis of the prototype circuit. Comparisons of the resulting algorithms to actual pedals show good agreement and demonstrate that the efficient algorithms presented reproduce the general character of the modeled pedals.
Download Simulation of the Diode Limiter in Guitar Distortion Circuits by Numerical Solution of Ordinary Differential Equations
The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (ODE). Numerical methods with stiff stability – Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula – allow the use of relatively low sampling rates at the cost of accuracy and aliasing. However, these methods require iteration at each time step to solve a nonlinear equation, and the tradeoff for this complexity must be evaluated against simple explicit methods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper surveys and compares the basic ODE solvers as they apply to simulating circuits for audio processing. These methods are compared to a static nonlinearity with a pre-filter. It is found that implicit or semiimplicit solvers are preferred and that the filter/static nonlinearity approximation is often perceptually adequate.
Download Spectral Dealy Filters with Feedback Delay Filters with Feedback and Time-Varying Coefficients
A recently introduced structure to implement a continuously smooth spectral delay, based on a cascade of first-order allpass filters and an equalizing filter, is described and the properties of this spectral delay filter are reviewed. A new amplitude envelope equalizing filter for the spectral delay filter is proposed and the properties of structures utilizing feedback and/or time-varying filter coefficients are discussed. In addition, the stability conditions for the feedback and the time-varying structures are derived. A spectral delay filter can be used for synthesizing chirp-like sounds or for modifying the timbre of arbitrary audio signals. Sound examples on the use of the spectral delay filters utilizing the structures discussed in this paper can be found at http://www.acoustics.hut. fi/publications/papers/dafx09-sdf/.
Download On Minimizing the Look-Up Table Size in Quasi-Bandlimited Classical Waveform Oscillators
In quasi-bandlimited classical waveform oscillators, the aliasing distortion present in a trivially sampled waveform can be reduced in the digital domain by applying a tabulated correction function. This paper presents an approach that applies the correction function in the differentiated domain by synthesizing a bandlimited impulse train (BLIT) that is integrated to obtain the desired bandlimited waveform. The ideal correction function of the BLIT method is infinitely long and in practice needs to be windowed. In order to obtain a good alias-reduction performance, long tables are typically required. It is shown that when a short look-up table is used, a windowed ideal correction function does not provide the best performance in terms of minimizing aliasing audibility. Instead, audibly improved alias-reduction performance can be obtained using a look-up table that has a parametric control over the low-order generations of aliasing. Some practical parametric look-up table designs are discussed in this paper, and their use and alias-reduction performance are exemplified. The look-up table designs discussed in this paper providing the best alias-reduction performance are parametric window functions and least-squares optimized multiband FIR filter designs.
Download Approximating Measured Reverberation Using A Hybrid Fixed/Switched Convolution Structure
An efficient reverberator structure is proposed for approximating measured reverberation. A fixed convolution matching the early portion of a measured impulse response is crossfaded with a switched convolution reverberator drawing its switched convolution section from the late-field of the measured impulse response. In this way, the early portion of the measured impulse response is precisely reproduced, and the late-field equalization and decay rates efficiently approximated. To use segments of the measured impulse response, the switched convolution structure is modified to include a normalization filter to account for the decay of the late-field between the nominal fixed/switched crossfade time and the time of the selected segment. Further, the measured impulse response late-field is extended below its noise floor in anticipation of the normalization. This structure provides psychoacoustically accurate synthesis of the measured impulse response using less than half a second of convolution, irrespective of the length of the measured impulse response. In addition, the structure provides direct control over the equalization and late-field frequency dependent decay rate. Emulations of EMT 140 plate reverberator and marble lobby impulse responses are presented.
Download A Physically-Informed, Circuit-Bendable, Digital Model of the Roland TR-808 Bass Drum Circuit
We present an analysis of the bass drum circuit from the classic Roland TR-808 Rhythm Composer, based on physical models of the device’s many sub-circuits. A digital model based on this analysis (implemented in Cycling 74’s Gen˜) retains the salient features of the original and allows accurate emulation of circuit-bent modifications—complicated behavior that is impossible to capture through black-box modeling or structured sampling. Additionally, this analysis will clear up common misconceptions about the circuit, support the design of further drum machine modifications, and form a foundation for circuit-based musicological inquiry into the history of analog drum machines.
Download Distortion and Pitch Processing Using a Modal Reverberator Architecture
A reverberator based on a room response modal analysis is adapted to produce distortion, pitch and time manipulation effects, as well as gated and iterated reverberation. The so-called “modal reverberator” is a parallel collection of resonant filters, with resonance frequencies and dampings tuned to the modal frequencies and decay times of the space or object being simulated. Here, the resonant filters are implemented as cascades of heterodyning, smoothing, and modulation steps, forming a type of analysis/synthesis architecture. By applying memoryless nonlinearities to the modulating sinusoids, distortion effects are produced, including distortion without intermodulation products. By using different frequencies for the heterodyning and associated modulation operations, pitch manipulation effects are generated, including pitch shifting and spectral “inversion.” By resampling the smoothing filter output, the signal time axis is stretched without introducing pitch changes. As these effects are integrated into a reverberator architecture, reverberation controls such as decay time can be used produce novel effects having some of the sonic characteristics of reverberation.
Download On Restoring Prematurely Truncated Sine Sweep Room Impulse Response Measurements
When measuring room impulse responses using swept sinusoids, it often occurs that the sine sweep room response recording is terminated soon after either the sine sweep ends or the long-lasting low-frequency modes fully decay. In the presence of typical acoustic background noise levels, perceivable artifacts can emerge from the process of converting such a prematurely truncated sweep response into an impulse response. In particular, a low-pass noise process with a time-varying cutoff frequency will appear in the measured room impulse response, a result of the frequency-dependent time shift applied to the sweep response to form the impulse response. Here, we detail the artifact, describe methods for restoring the impulse response measurement, and present a case study using measurements from the Berkeley Art Museum shortly before its demolition. We show that while the difficulty may be avoided using circular convolution, nonlinearities typical of loudspeakers will corrupt the room impulse response. This problem can be alleviated by stitching synthesized noise onto the end of the sweep response before converting it into an impulse response. Two noise synthesis methods are described: the first uses a filter bank to estimate the frequency-dependent measurement noise power and then filter synthesized white Gaussian noise. The second uses a linearphase filter formed by smoothing the recorded noise across perceptual bands to filter Gaussian noise. In both cases, we demonstrate that by time-extending the recording with noise similar to the recorded background noise that we can push the problem out in time such that it no longer interferes with the measured room impulse response.
Download Constrained Pole Optimization for Modal Reverberation
The problem of designing a modal reverberator to match a measured room impulse response is considered. The modal reverberator architecture expresses a room impulse response as a parallel combination of resonant filters, with the pole locations determined by the room resonances and decay rates, and the zeros by the source and listener positions. Our method first estimates the pole positions in a frequency-domain process involving a series of constrained pole position optimizations in overlapping frequency bands. With the pole locations in hand, the zeros are fit to the measured impulse response using least squares. Example optimizations for a mediumsized room show a good match between the measured and modeled room responses.