A Novel Method for Generating Complex Half-Band Filters

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 generalized 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. Furthermore, we derive the closed form expression of the filter frequency response, thereby providing an analytical foothold into filter characteristics. For determining filter performance, we focus on the spacial shiftability [12] property of the filter and compare it with that of other filter designs. Using a total variation measure for determining function variation, we see that its shiftability typically either matches or exceeds that of other methods. Furthermore, this design method lends itself to an enhancement [2], 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 uniformly to the ideal complex half-band amplitude spectrum as N → + ∞ except at 0 and π, where it converges pointwise to 1, thereby assuring full shiftability