High-Precision Digital Audio Waveform Synthesis Using a Multi-Frequency Interpolation Technique

Abstract

A description is given of a digital, real-time, multi-frequency function generator for audio bandwidth applications. A novel feature of the system is the embedded algorithm, which employs a bank of parallel interpolators, rather than a look-up table, to synthesise complex functions with high precision and fl exibility. The complete instrumentation comprises a high-level software design tool operating on a conventional desktop or notebook PC and a separate hardware unit incorporating a powerful real-time digital signal processor unit, operating at 275 million multiplication-accumulations per second (MMACs) and a dual channel 24-bit codec with a maximum output rate of 200 kilo-samples per second. Using total harmonic distortion (THD) analysis, the purity of the waveforms has been compared with those generated by traditional analogue instruments; this analysis has confi rmed that the new instrument has a consistently superior performance over such devices. Testing established that for a 2 kHz sine wave, for example, there was an order of magnitude improvement in THD performance over a commercially available analogue function generator. The algorithm and associated hardware offer the combined advantages of function fl exibility, ease of implementation, accuracy and the unique ability to alter, in real-time, the frequencies, magnitudes and phases of individual harmonics within any given arbitrary waveform. Digital function generation and waveform synthesis represent key components of any DSP course; at the University of Manchester it is taught as a formal discipline through lectures, and from a practical context during our laboratory classes, in which students gain an understanding of digital methods and how they excel over traditional analogue circuits designed for the same purpose.