Extracting real samples from complex sampled data

The process of employing a discrete Hilbert transform to derive a complex data stream from a real data stream has been described in the literature but not the converse operation. A technique is provided to construct an equivalent real data set from a complex data set which guarantees by construction that the proper symmetry conditions on the Fourier transform of the data set are met. The technique is also useful for computing the real impulse response associated with a complex transfer function.