This paper proposes the use of chirp-z transform (CZT) in spectrum sensing to achieve higher frequency resolution in spectrum monitoring. The CZT method can efficiently utilize the dispersed frequency spectrum of any desired band of interest. The performance of the proposed system over additive white Gaussian noise (AWGN) and Rayleigh channels is analyzed and presented through ROC curves. In order to maximize the total error rate performance of the proposed system, the optimal detection threshold expressions are derived in the case of AWGN and Rayleigh faded channels. Afterwards, the optimal detection threshold expressions are validated by simulation and numerical results.