Abstract: The amount of memory needed for a ROM-based .pi./4 DQPSK filter is reduced by using a mapper in an IQ modulator (inverse mapper in a demodulator) that incorporates a 90.degree. phase shift for every other symbol. During the intervening symbols no additional phase shift is incorporated by the mapper. This produces a coarse precession of 90.degree. for every other symbol. The 90.degree. of coarse precession may be produced by using alternate DQPSK mappers for alternate symbols. Both mappers share a common repertoire, so no new modulation state symbols are required. During the alternate 0.degree. symbols the filter inserts a 45.degree. phase shift, but does not insert such a 45.degree. phase shift during those intervening times when the mapper (or inverse mapper) is inserting a 90.degree. phase shift. This produces a fine precession. The result is to produce a uniform precession of 45.degree. between each modulation state symbol.