ON THE FFT OF 1-BIT DITHER-QUANTIZED DETERMINISTIC SIGNALS

Abstract

Reducing the quantization resolution of the FFT input is bound to adversely affect its computational accuracy. This loss in accuracy will in turn prohibit exploiting the practical advantages that an FFT algorithm, with a coarsely-quantized input, will otherwise enjoy. This paper proposes a new theory that allows the use of coarse quantization with only a negligible effect on the FFT computational accuracy. The proposed theory is tested on deterministic signals that undergo the crudest quantization possible (i.e. 1 bit) and is very well supported by the simulation results. Finally, these results provide a strong encouragement to extend this theory to noisy signals as well as to numerous other important transforms.