An efficient algorithm for analytic signal generation for time-frequency distributions

Abstract

In this paper we discuss methods to produce the discrete analytic signal from a discrete real-valued signal. An analytic signal associated with a real signal is a complex signal which contains only positive frequencies and whose projection onto the real axis is the same as the original signal. There are many applications where analytic signals are useful, including the field of communication systems. Our use stems from instantaneous-frequency estimation and time-frequency signal analysis problems. For these problems the negative frequency component of real signals causes unwanted interference. The task of designing a filter to produce an approximation to the ideal analytic signal is not as simple as its formulation might suggest. Our result is that the direct methods of zeroing the negative frequencies, or using Hilbert transform filters, have undesirable defects. We present an alternative, which is similar to the 'quadrature' filters used in modem designs. >