On the design of optimal orthogonal finite order transmitter and receiver filters for data transmission over noisy channels

The design of orthogonal multirate finite order digital filters for data transmission over noisy channels has received considerable attention, due to the fact that, these filters play a key role in multicarrier communication systems such as xDSL and CDMA. The problem of designing such filters for maximum energy concentration in the channel bandwidth is revisited. The key constraint in this work is the computational efficiency of the filter design procedure as well as the cost of implementing the filter. For the FIR case, we propose a new semidefinite program (SDP) formulation. The SDP finds the globally optimum product filter H(z)H(z/sup -1/) and is more efficient than the existing solution. A new characterization of the minimum phase spectral factor H/sub min/(z) is also presented. We then consider the optimum design of a special class of IIR multirate filters, namely the class of IIR filters that are the sum of two all pass. Despite its constrained nature, we show that a low order IIR filter can be as "spectrally efficient" as an FIR filter with much more parameters.