Application of Undersampled Hilbert Transform to Complex Modulated Signals

In technical processes signals are very often complex modulated. A typical example is an ultrasonic wave passing a streaming fluid perpendicularly which is superposed by stochastically distributed turbulences. The demodulation of the signal can be carried out by digital undersampling to separate the narrow sidebands to the carrier frequency in the frequency domain. The complex signal can be divided into real and imaginary parts by application of Hilbert transform. The imaginary part of the signal can not be obtained directly through the measurement but needs a transform from the measured real part. This procedure is called Hilbert transform. Based on the normal digital Hilbert transform, an undersampled Hilbert transform is presented in this paper as well as its results and conclusions which are drawn from the method