Various ways to implement infinitely rising or falling spectral notches, also known as the barberpole phaser and flanging illusions, are described and studied. The first method is inspired by the Shepard-Risset illusion, and is based on a series of several cascaded notch filters moving in frequency one octave apart from each other. The second method, called a synchronized dual flanger, realizes the desired effect in an innovative and economic way using two cascaded time-varying comb filters and cross-fading between them. The third method is based on the use of single-sideband modulation, also known as frequency shifting. The proposed techniques effectively reproduce the illusion of endlessly moving spectral notches, particularly at slow modulation speeds and for input signals with a rich frequency spectrum. These effects can be programmed in real time and implemented as part of a digital audio processing system.

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A method to measure the response of a linear time-variant (LTV) audio system is presented. The proposed method uses a series of short chirps generated as the impulse response of several cascaded allpass filters. This test signal can measure the characteristics of an LTV system as a function of time. Results obtained from testing of this method on a guitar phaser pedal are presented. A proof of concept gray-box model of the measured system is produced based on partial knowledge about the internal structure of the pedal and on the spectral analysis of the measured responses. The temporal behavior of the digital model is shown to be very similar to that of the measured device. This demonstrates that it is possible to measure LTV analog audio systems and produce approximate virtual analog models based on these results.

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The use of the bandlimited ramp (BLAMP) function as an antialiasing tool for audio signals with sharp corners is presented. Discontinuities in the waveform of a signal or its derivatives require infinite bandwidth and are major sources of aliasing in the digital domain. A polynomial correction function is modeled after the ideal BLAMP function. This correction function can be used to treat aliasing caused by sharp edges or corners which translate into discontinuities in the first derivative of a signal. Four examples of cases where these discontinuities appear are discussed: synthesis of triangular waveforms, hard clipping, and half-wave and fullwave rectification. Results obtained show that the BLAMP function is a more efficient tool for alias reduction than oversampling. The polynomial BLAMP can reduce the level of aliasing components by up to 50 dB and improve the overall signal-to-noise ratio by about 20 dB. The proposed method can be incorporated into virtual analog models of musical systems.

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An antialiased digital model of the wavefolding circuit inside the Buchla 259 Complex Waveform Generator is presented. Wavefolding is a type of nonlinear waveshaping used to generate complex harmonically-rich sounds from simple periodic waveforms. Unlike other analog wavefolder designs, Buchla’s design features five op-amp-based folding stages arranged in parallel alongside a direct signal path. The nonlinear behavior of the system is accurately modeled in the digital domain using memoryless mappings of the input–output voltage relationships inside the circuit. We pay special attention to suppressing the aliasing introduced by the nonlinear frequency-expanding behavior of the wavefolder. For this, we propose using the bandlimited ramp (BLAMP) method with eight times oversampling. Results obtained are validated against SPICE simulations and a highly oversampled digital model. The proposed virtual analog wavefolder retains the salient features of the original circuit and is applicable to digital sound synthesis.

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This paper proposes signal processing methods to extend a stationary part of an audio signal endlessly. A frequent occasion is that there is not enough audio material to build a synthesizer, but an example sound must be extended or modified for more variability. Filtering of a white noise signal with a filter designed based on high-order linear prediction or concatenation of the example signal can produce convincing arbitrarily long sounds, such as ambient noise or musical tones, and can be interpreted as a spectral freeze technique without looping. It is shown that the random input signal will pump energy to the narrow resonances of the filter so that lively and realistic variations in the sound are generated. For realtime implementation, this paper proposes to replace white noise with velvet noise, as this reduces the number of operations by 90% or more, with respect to standard convolution, without affecting the sound quality, or by FFT convolution, which can be simplified to the randomization of spectral phase and only taking the inverse FFT. Examples of producing endless airplane cabin noise and piano tones based on a short example recording are studied. The proposed methods lead to a new way to generate audio material for music, films, and gaming.

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