I was always surprised to see the wide price differences between HP vintage oscilloscopes and HP spectrum analyzers from the same period. So it was with excitement that I got a HP 8591E spectrum analyzer for our shop.
Nowadays most of the current oscilloscopes have some kind of spectrum analysis tools - always performed as FFT (fast fourier transforms) of the waveform readings. These machines use a completely different method. I will copy from wikipedia so as to be able to explain it better:
A swept-tuned analyzer uses a superheterodyne receiver to down-convert a portion of the input signal spectrum to the center frequency of a narrow band-pass filter, whose instantaneous output power is recorded or displayed as a function of time. By sweeping the receiver's center-frequency (using a voltage-controlled oscillator) through a range of frequencies, the output is also a function of frequency. But while the sweep centers on any particular frequency, it may be missing short-duration events at other frequencies.
In future installments I will discuss this wonderful machine - complementary but completely different to your oscilloscope.