Efficient convolution via FFT with real-to-complex packing

We propose a method to reduce computation time for FFT-based convolution by a factor of two when both input signals are real. In general the proposed method can be applied to any real signals. In case when the convolution kernel has odd or even symmetry, the method can be simplified even further. We improve convolution speed by packing real signals of size N into a complex signal of size N/2 and performing the N-size FFT. Note that traditional FFT-based convolution requires FFT of size 2N. The convolution time with the Hilbert kernel reduces from 30.3 seconds to 13.5 seconds for 160 thousand convolutions of 1024-size datasets on CPU.