A spectrum analyzer (10, 70) employs a method of reducing the amplitude of harmonic and spurious signals (102, 104, 112) introduced into a frequency-domain output spectrum by, for example, nonlinearities in a mixer (12, 78) or an ADC (20, 92). The method employs acquiring and digitizing a normal time-domain data record of an input signal, transforming the time-domain data record to a normal frequency-domain record (30), and storing the normal record. Next, a local oscillator (14, 76) driving the mixer is frequency shifted, and an additional time-domain data record is acquired, digitized, transformed, and stored to produce a shifted frequency-domain data record (40). Then, the shifted data record is mathematically realigned (50) with the normal data record and the normal and realigned data records are combined to produce a frequency-domain data record (60) having reduced harmonic and spurious signal amplitudes. The method preferably employs multiple frequency shifts of the local oscillator and a corresponding number of acquisitions, digitizations, transformations, realignments, and averages.