Band-Limited Impulse Train Generation Using Sampled Infinite Impulse Responses of Analog Filters

Abstract

The oscillator or waveform generator is at the heart of the musical sound synthesizers technology. A digital oscillator is the discrete time counterpart of the analog voltage control oscillator. A band-limited oscillator (BLO) is a digital oscillator that explicitly limits the power of the aliasing artifacts. It aims at reproducing on a Digital Signal Processor (DSP) the popular waveforms such as pulse-width modulated (PWM) square, sawtooth or triangle waveforms. The generation of a band-limited impulse train (BLIT) is central to most BLO algorithms. Most BLIT algorithms are based on finite impulse response (FIR) filters. The paper presents an innovative scheme for constructing a BLIT based on infinite impulse response (IIR) filters which have better stopband rejection performances. The BLIT is actually obtained by emulating the sampling at an arbitrary sampling rate of an impulse train filtered by an analog IIR filter. The method is flexible because, at the end, it relies on the classical design of an analog low-pass filter. Furthermore the complexity of the method is not impacted by the length of the impulse response. Finally, as for most BLIT based methods, the power of the aliasing artifacts is reduced even in case of frequency or pulse width modulation in the audio range.