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A band-limited signal can be represented by the real and complex zeros of the signal. By simple invertible techniques, it is possible to convert the signal into another one which has only real (physical) zeros. Based on a zero-based representation, a spectrum analyzer is proposed. The spectrum analyzer samples the zero crossings of the signal waveform and uses this information to determine the discrete Fourier transform coefficients in software. The zero-based spectrum analyzer alleviates many of the shortcomings of the conventional A/D converter-based spectrum analyzer. In particular, the hardware is simple and the dynamic range and speed limitations of the A/D converter are reduced. The results of a computer simulation study of the error aspects of the spectrum analyzer are presented.