Design and implementation of transmitter and receiver filters with periodic coefficient nulls for digital systems

The problem of designing nonrecursive digital filters to perform baseband and passband pulse shaping in digital systems amounts to determining a discrete sequence with preassigned zero crossings. This approach yields a filter frequency response which permits minimal stop band noise enhancement. Several methods exist for designing transmitter and receiver filters for digital systems. An interesting technique using a minimax criterion in the design procedure employs linear programming techniques in the frequency domain, in addition to ensuring periodic nulls in the time domain. We derive a bound which gives insight into the frequency resolution or frequency sampling grid density problem, and also provides an analytical basis for determining an estimate of the filter length. Problems encountered with efficient transmitter implementation are discussed along with methods found useful in overcoming these problems.