Synthesis of sinusoids via non-overlapping inverse Fourier transform

Additive synthesis is a powerful tool for the analysis/modification/synthesis of complex audio or speech signals. However, the cost of wavetable sinusoidal synthesis can become prohibitive for large numbers of sinusoids (more than a few hundred). In that case, techniques based on the inverse Fourier transform offer an attractive alternative, being 200-300% more efficient than wavetable synthesis depending on the number of sinusoids. This paper presents an improved technique based on the concatenation of short-term signals obtained by inverse Fourier transforms. In contrast to the standard overlap-add technique, the new algorithm requires synthesizing sinusoids in the frequency domain whose time-domain amplitudes vary linearly within the synthesis frame. The technique is shown to achieve higher quality than the standard overlap-add technique, at the cost of a small increase in computation.