A Nonrecursive Approach for Zero Crossing Based Spectral Analysis

The spectral analysis of a band-limited signal can be achieved by means of a zero crossing approach without explicit analog-to-digital conversion. For this, a pure sinusoid is added to the signal to be analyzed. In this letter, it is shown that the cost for computing the spectrum can be significantly reduced and multiplicative recursions can be avoided if the frequency of the additional sinusoid is at least twice the band limit of the signal. In the limit case, for very small input signals, the computation method presented here is converging toward the computation of a discrete Fourier transform. It is demonstrated that the noise introduced by the quantization of the time axis is spectrally white.