Abstract: A novel method and apparatus for computing the phase derivative and also the frequency of a received signal from digital baseband In-Phase (I) and Quadrature (Q) samples is derived and implemented. The resulting method computes the phase derivative and frequency of a received signal from I and Q data directly without the intermediate problem of phase unwrapping required for computing the derivative of modulo-mapped phase. The apparatus is intended for use both in single channel systems performing digital frequency demodulation and in direction-finding systems computing differential phase across two channels.