In a nonideal PLL circuit, leakage of the reference signal into the control line produces spurious tones. When the distorted PLL signal is used in an analog-to-digital converter (ADC), it injects the spurious tones into the sampled data. These distortions are particularly harmful for wideband applications, such as spectrum sensing, since they affect the detection of vacant frequency bands. This paper analyzes this distortion effect in some detail and proposes estimation and filtering techniques in the digital domain to clean the data and remove the PLL leakage effects. Rather than remove the PLL sidebands by perfecting the circuitry, the proposed approach focuses on compensating their effect on the sampled data by using signal processing compensation algorithms. We study the performance of the proposed estimation algorithms and compare it with the corresponding Cramer-Rao bound (CRB). Such digitally based approaches are cost effective since the cost of perfecting the analog circuits can be prohibitive due to regular variations and imperfections in circuit fabrication processes.