The sliding DFT process for spectrum analysis was presented and shown to be more efficient than the popular Goertzel (1958) algorithm for sample-by-sample DFT bin computations. The sliding DFT provides computational advantages over the traditional DFT or FFT for many applications requiring successive output calculations, especially when only a subset of the DFT output bins are required. Methods for output stabilization as well as time-domain data windowing by means of frequency-domain convolution were also discussed. A modified sliding DFT algorithm, called the sliding Goertzel DFT, was proposed to further reduce the computational workload. We start our sliding DFT discussion by providing a review of the Goertzel algorithm and use its behavior as a yardstick to evaluate the performance of the sliding DFT technique. We examine stability issues regarding the sliding DFT implementation as well as review the process of frequency-domain convolution to accomplish time-domain windowing. Finally, a modified sliding DFT structure is proposed that provides improved computational efficiency.