Systems and methods for digital signal processing using a sliding windowed infinite Fourier transform (“SWIFT”) algorithm are described. A discrete-time Fourier transform (“DTFT”) of an input signal is computed over an infinite-length temporal window that is slid from one sample in the input signal to the next. The DTFT with the temporal window at a given sample point is effectively calculated by phase shifting and decaying the DTFT calculated when the temporal window was positioned at the previous sample point and adding the current sample to the result.