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Although most applications which use the short-time Fourier transform (STFT) temporally downsample the output, some applications exploit a dense temporal sampling of the STFT. One example, coded-division multiple-beam sonar, is discussed. Given a need for the densely sampled STFT, the complexity of the computation can be reduced from O(N log N) for the general short-time FFT structure to O(N) using the Goertzel algorithm. The authors introduce the pruned short-time FFT, a novel computational structure for efficiently computing the STFT with dense temporal sampling. The pruned FFT achieves the same computational savings as the Goertzel algorithm, but is unconditionally stable.