A Novel Method for Generating Complex Half-Band Filters

M. Elfataoui and Gagan Mirchandani

We propose a simple, novel and efficient method for generating complex half-band FIR filters, which we use in the generation of discrete-time analytic (DTA) signals. These filters have properties of linear phase and real-time implementation while the DTA signals generated are orthogonal and invertible (the original real signal is recoverable). The filter design, in contrast to some other methods, is easily scalable and stable. The new method is evaluated for performance (i.e. aliasing) by comparing its shiftability \cite{simoncelli} property with that of other transforms. Using a total variation measure for determining function variation, we see that its shiftability either matches or exceeds that of other methods. Furthermore, this design method lends itself to an enhancement \cite{melfataoui}, thereby allowing additional improvement in shiftability. We prove an important theoretical aspect of the new method: the amplitude spectrum of the length-$N$ filter converges almost everywhere to the ideal complex half-band amplitude spectrum as $N \rightarrow +\infty$, thereby assuring shiftability.