In this paper, we propose a method for extracting the spectral information of a multi-gigahertz jittery signal. This method utilizes existing on-chip single-shot period measurement techniques to sample and measure the period of multiple cycles of the multi-gigahertz periodic signal for spectral analysis. Since measurements are made on the period of multiple cycles, but not on the period of a single cycle, a lower-speed timing measurement circuitry can be used to measure a higher-speed signal. Therefore, the proposed solution is scalable for even higher-speed signals. This method does not require an external sampling clock, nor any additional measurement beyond existing techniques. Experimental results based on simulation show that this method can accurately estimate the sinusoidal and random jitters of a multi-gigahertz signal.