Spectrally rich phase distortion sound synthesis using an allpass filter

Timoney, Joseph; Lazzarini, Victor; Pekonen, Jussi; Välimäki, Vesa

doi:10.1109/icassp.2009.4959578

Cited by 4 publications

(8 citation statements)

References 3 publications

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“…The first discrete-time model of the Moog sawtooth waveform oscillator proposed here is based on direct time-domain modelling of the target waveform using phase distortion (PD) synthesis [23][24][25][26]. In PD synthesis, the normally linear f 0 -dependent phase trajectory φ lin (t) of a sinusoid is modified with a nonlinear shaping function f (x), that is, the phase distorted sinusoid is given by…”

Section: Waveform-based Modelling Using Phase Distortion Synthesismentioning

confidence: 99%

“…where t is time and φ 0 is the initial phase. This approach is effectively the same as phase (or frequency) modulation as the phase shaping function can be decomposed into a linear part and a time-varying component [24][25][26] as…”

Section: Waveform-based Modelling Using Phase Distortion Synthesismentioning

confidence: 99%

“…where P ∈ [0, 1] is the fraction of the period during which the sawtooth function is rising [24,25]. Applying (2) and (3) to (1) yields…”

Section: Waveform-based Modelling Using Phase Distortion Synthesismentioning

confidence: 99%

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Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Pekonen

Lazzarini

Timoney

et al. 2011

EURASIP J. Adv. Signal Process.

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Discrete-time modelling strategies of analogue Moog sawtooth oscillator waveforms are presented. Two alternative approaches suitable for real-time implementation are proposed, one modelling the analogue waveform in time domain using phase distortion synthesis and another matching the spectrum of an existing antialiasing sawtooth oscillator to the corresponding analogue spectrum using a first-order IIR post-equalising filter. A parameter estimation procedure for both approaches is explained and performed. Performance evaluation using polynomial fits for the estimated parameters is carried out, and good matches between the model outputs and recorded waveforms are obtained. The best match of the tested algorithms is produced by the phase distortion model and by post-equalising the fourth-order B-spline bandlimited step function sawtooth oscillator.

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Section: Waveform-based Modelling Using Phase Distortion Synthesismentioning

confidence: 99%

Section: Waveform-based Modelling Using Phase Distortion Synthesismentioning

confidence: 99%

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Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Pekonen

Lazzarini

Timoney

et al. 2011

EURASIP J. Adv. Signal Process.

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“…The filter defined by (9) and 10is therefore equivalent to a filter of length N, made up of a cascade of a time-varying FIR filter of order N − 1 and coefficients b k (n), and an IIR (comb) filter with a fixed coefficient a N . The equivalent filter equation is, thus,…”

Section: Filter Interpretationmentioning

confidence: 99%

Feedback Amplitude Modulation Synthesis

Kleimola

Lazzarini

Välimäki

et al. 2010

EURASIP J. Adv. Signal Process.

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A recently rediscovered sound synthesis method, which is based on feedback amplitude modulation (FBAM), is investigated. The FBAM system is interpreted as a periodically linear time-varying digital filter, and its stability, aliasing, and scaling properties are considered. Several novel variations of the basic system are derived and analyzed. Separation of the input and the modulation signals in FBAM structures is proposed which helps to create modular sound synthesis and digital audio effects applications. The FBAM is shown to be a powerful and versatile sound synthesis principle, which has similarities to the established distortion synthesis methods, but which is also essentially different from them.

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“…12 Alternatively, the waveforms can be synthesized from a sinusoid by means of distortion synthesis [13][14][15] in which the higher harmonics are generated by applying a nonlinear waveshaper 16,17 or phase distortion 18,19 to the sinusoid having the desired fundamental frequency. The phase distortion approach using a time-varying first-order allpass filter 14,19,20 has been extended to a chain of time-varying allpass filters. 21 Other nonlinear approaches to the approximation of these classical waveforms include the use of a nonlinear waveshaper in the feedback path of a feedback amplitude modulation synthesizer 22 and bitwise logical modulation of two sinusoidal oscillators.…”

Section: Introductionmentioning

confidence: 99%

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

Välimäki

Pekonen

Nam

2012

The Journal of the Acoustical Society of America

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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.

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Spectrally rich phase distortion sound synthesis using an allpass filter

Cited by 4 publications

References 3 publications

Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Discrete-Time Modelling of the Moog Sawtooth Oscillator Waveform

Feedback Amplitude Modulation Synthesis

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

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