An improved sliding discrete Fourier transform (SDFT) algorithm called CIC-SDFT and its apparatus are provided. An input signal is multiplied by a modulated twiddle factor, and is then processed by a modified cascade integrator-comb (CIC) filter. The CIC-SDFT comprises an integrator section and a comb section, with a downsampler disposed between the two sections to enable downsampling of the SDFT computations. Through addition of more integrator stages and comb stages to the CIC-SDFT, the accuracy of spectrum estimation may be improved in a computationally inexpensive manner and with less complexity than applying windowing functions to known SDFTs. Various embodiments provide a partially-nonrecursive method of CIC-SDFT that further decreases computational complexity.