A novel and fast 1-bit FFT scheme with two dither-quantized channels

The paramount importance enjoyed by the FFT algorithm and its variants is amply demonstrated by the plethora of applications it currently enjoys in a myriad of practical areas. As this algorithm is invariably digitally implemented, its computational accuracy relies on its two inputs having a sufficiently fine quantization. This precludes the use of a coarse quantization scheme for the 2 FFT inputs and the exploitation of all the concomitant and attractive practical advantages that this scheme would bring to the FFT application at hand. This paper proposes a new theory that resolves this conflict between exploiting these practical advantages and retaining an acceptable computational accuracy of the FFT. This theory is tested with the smallest possible quantization resolution (1-bit) at which all potential practical advantages are maximized. The simulation work, which includes both clean and noisy signals, corroborates the proposed theory quite well even in severely noisy environments.