The DFT is typically held as too slow for direct computation. However, for small windows of time, on even modest machines and voice-grade single-channel 8-bit audio, we find that the computation can be fast enough for real-time processing.
Journal of Object Technology
Lyon, Douglas A., "The Discrete Fourier Transform, Part 1" (2009). Engineering Faculty Publications. 76.
Douglas Lyon, “The Discrete Fourier Transform, Part 1”, Journal of Object Technology, Volume 8, no. 3 (May 2009), pp. 17-26