Optimized Sinusoid Synthesis via Inverse Truncated Fourier Transform

Abstract

It was shown that sinusoid synthesis can be implemented efficiently by an inverse Fourier transform on consecutive frames where all but a small number of coefficients per oscillator are dropped. This leads to a compromise between computational complexity and approximation accuracy. The method can be improved by two approaches. First, optimal coefficients can be found by minimizing the average approximation error. Second, the optimal window function can be found through an iterative process. The gain in signal-to-noise ratio (SNR) is between 10 and 40 dB and can be used to reduce computational complexity while satisfying required synthesis quality.