Precise Complex Tone Generation by Digital Table-Lookup Techniques
S.A. White · The Journal of the Acoustical Society of America · 1973
Complex arbitrary periodic waveforms may be generated by simple table-lookup means. An important trade-off exists between the number of points of that waveform which is stored in the memory and the interpolation complexity. A simple frequency-generation technique is analyzed, and the attendant accuracy requirements (word length) are developed. Next, the relationship between the amplitude of the points stored to represent the waveform and its frequency spectrum are derived in a review of the discrete Fourier transform. The transfer functions (and frequency responses) of the buffers associated with the memory and the interpolator, as well as the transfer functions of the interpolators proper are derived. Shown also are the effects on the frequency response of the generator system as a function of the number of interpolation points and the order of the interpolator. The mathematical model of the interpolator is in exact agreement with measured data. The system is easily mechanized by a read-only memory, an accumulator, adders, and simple logic. Applications have been to communications, sonar, vibration testing, and music synthesis.