Chris@3:
Chris@7:
Chris@7:
Chris@3:
Chris@1:
Chris@3:
Chris@3:
Chris@3:
Chris@3:
Chris@3:
Chris@3:
Chris@7:
Chris@7:
Chris@8:
Chris@8:
Chris@3:
Chris@1:
Chris@7:
Chris@3:
Chris@2:
Chris@3: Results
Chris@1:
Chris@3:
Chris@3:
Chris@3:
Chris@3:
Chris@3: | Implementation | Result | Time (first half) | Time (second half) | Rate (second half) |
Chris@3:
Chris@3:
Chris@3: | Nayuki | | | | |
Chris@3:
Chris@3: | Nockert | | | | |
Chris@3:
Chris@3: | Dntj | | | | |
Chris@7:
Chris@7: | Cross | | | | |
Chris@8:
Chris@8: | KissFFT | | | | |
Chris@3:
Chris@3:
Chris@1:
Chris@3: Notes
Chris@1:
Chris@3:
Chris@3: - Nayuki: in-place single-precision complex-complex
Chris@3: - Nockert: double-precision real-complex
Chris@10: - Nayuki: double-precision complex-complex. Forward
Chris@10: transform is scaled and I've scaled it back again here, which may
Chris@10: introduce rounding error.
Chris@10: - Cross: double-precision real-complex in C, compiled
Chris@10: with Emscripten. This is considered a slow implementation amongst
Chris@10: native code ones.
Chris@10: - KissFFT: single-precision real-complex in C, compiled
Chris@10: with Emscripten. This should be faster than Cross. Despite its
Chris@10: name, it is the most sophisticated implementation here.
Chris@3:
Chris@3:
Chris@3: Rationale
Chris@1:
Chris@3: If 2150 iterations of real-to-complex FFT of size 2048 takes less
Chris@3: than 10 seconds, then we may be able to make a high quality
Chris@3: real-time phase vocoder (just).
Chris@1:
Chris@3: A phase-vocoder of course must use overlapped windowed FFT
Chris@3: (although you can choose the size, within limits), IFFT, and
Chris@3: cartesian-polar conversion to calculate the phase for the
Chris@3: instantaneous frequency.
Chris@1:
Chris@3: A reasonable estimate of CPU cost for the whole thing is
Chris@3: somewhere around 10x the cost of simple non-overlapping short-time
Chris@3: forward Fourier transforms across the signal.
Chris@1:
Chris@3: 2150 iterations corresponds to 100 seconds of audio
Chris@3: non-overlapped at 44.1kHz, so if that takes less than 10 seconds,
Chris@3: then in theory we might be OK.
Chris@1:
Chris@3:
Chris@1: