An all-optical sampling based on a semiconductor optical amplifier Mach–Zehnder interferometer is performed. The frequency properties of a sampled signal are exploited to obtain both frequency up-conversion and frequency down-conversion of quadrature phase shift keying (QPSK) data. An optical pulse source, generating 10-ps-width pulses at a repetition rate of 7.8 GHz used as a sampling signal, allows operation in the range of 0.5–39.5 GHz. The conversion gain of the all-optical sampling mixer is measured over the whole frequency range. It varies over this range from 20.4 to 0 dB for frequency down-conversion and from 15.5 to − 13.4 dB for frequency up-conversion. QPSK data at symbol rates between 8 and 128 MSymb/s are frequency converted. The Error Vector Magnitude is used to evaluate the quality of the frequency conversion. Exploitable error vector magnitudes (EVMs) in the range of 14% to 27.4% are reached for frequency up-conversion to the higher target frequency for all the symbol rates. For down-conversion, the EVM varies from 6.7% to 29.2% at the symbol rate of 64 MSymb/s for the whole frequency range. By using a differential configuration, the conversion gain is improved by 8.6 and 9 dB for up-conversion and down-conversion operations, respectively. The benefit provided by the differential configuration leads to a better EVM. Its value is shifted by almost 11% for frequency up-conversion and frequency down-conversion of data at a symbol rate of 64 MSymb/s.