A new, fast and low-cost FFT estimation scheme of signals using 1-bit non-subtractive dithered quantization

This paper studies the use of coarse quantization schemes, and the exploitation of their associated practical advantages, in the computation of one of the cornerstone algorithms in digital signal processing (DSP), i.e., the FFT algorithm. Such advantages include low structural complexity, low implementational cost and high computational speed. However, as the quantization resolution gets smaller, the irreversible loss in computational accuracy becomes more prohibitive, thus precluding the use of these attractive practical advantages. We propose here a new theory which will allow the use of any coarse quantization scheme, including the crudest possible (i.e. 1-bit) while, in practice, incurring only a negligibly small loss in accuracy. The proposed theory hinges on the use of dithered quantization scheme. The 1-bit version of this theory has been successfully tested on simulated and real signals, including music and speech signals, as evidenced by our simulation results. Finally, these results provide a strong encouragement to extend this theory to noisy signals as well as to numerous other important transforms.